When data are presented using a scatter plot that is fitted with a trend line, we can calculate estimations based on the association between variables. Several conditions must be met before one can use a scatter plot to make estimates off of correlations.

First, the points must possess some type of relationship between one another. This relationship can be positive or negative. Positive relationships occur when data move upwards from the left side to the right side of the graph; however, when the data slopes downward the relationship is negative. Second, we must identify if the relationship is strong or weak. A strong correlation exists when the data is clustered closer together and the trend line. On the other hand, a weak correlation occurs when data is spread apart from each other and the trend line. After we have evaluated these characteristics of the graph, we can use the scatter plot to make predictions.

How do we make predictions? Predictions are made using several methods: qualitative and quantitative observations. One can qualitatively use the associations present in the graph to make estimates based on spread, clustering, and the trend line’s position. Spread between points in a given area can provide a range of values for a given coordinate, while clustering of plots in a given area can give an average value for a given coordinate. On the other hand, the trend line can be used to estimate points by drawing lines that intersect from each axis. Last, we can quantitatively estimate a point using the equation of the trend line and solving for either the x- or y-variable.

Let’s work with these methods and solve the question.

First let’s observe if we can make a prediction using the following data:

We can see that the data possesses a positive correlation: that is, as the runner’s weight increases then so does the time it takes them to run a mile. Also, we can see that the points are weakly to moderately clustered with one another and the trend line; therefore, we can use qualitative and quantitative means to estimate how fast a 197 pound male can run a mile.

Next, let’s make a qualitative estimate by drawing a line from 197 pounds on the x-axis to the trend line. Next, we will draw a line from that point to the y-axis. This will qualitatively estimate our value. Observe this method below:

Now, lets predict this value quantitatively using the equation of the line:

Plug in 197 for the x-coordinate.

Solve

Round to two decimal places.

According to the data, we can predict that it would take a male 8.77 minutes for a 197 pound male to run a single mile.

Remember, we can also use this method to estimate the y-value of the data.

When data are presented using a scatter plot that is fitted with a trend line, we can calculate estimations based on the association between variables. Several conditions must be met before one can use a scatter plot to make estimates off of correlations.

First, the points must possess some type of relationship between one another. This relationship can be positive or negative. Positive relationships occur when data move upwards from the left side to the right side of the graph; however, when the data slopes downward the relationship is negative. Second, we must identify if the relationship is strong or weak. A strong correlation exists when the data is clustered closer together and the trend line. On the other hand, a weak correlation occurs when data is spread apart from each other and the trend line. After we have evaluated these characteristics of the graph, we can use the scatter plot to make predictions.

How do we make predictions? Predictions are made using several methods: qualitative and quantitative observations. One can qualitatively use the associations present in the graph to make estimates based on spread, clustering, and the trend line’s position. Spread between points in a given area can provide a range of values for a given coordinate, while clustering of plots in a given area can give an average value for a given coordinate. On the other hand, the trend line can be used to estimate points by drawing lines that intersect from each axis. Last, we can quantitatively estimate a point using the equation of the trend line and solving for either the x- or y-variable.

Let’s work with these methods and solve the question.

First let’s observe if we can make a prediction using the following data:

We can see that the data possesses a positive correlation: that is, as the runner’s weight increases then so does the time it takes them to run a mile. Also, we can see that the points are weakly to moderately clustered with one another and the trend line; therefore, we can use qualitative and quantitative means to estimate how fast a 239 pound male can run a mile.

Next, let’s make a qualitative estimate by drawing a line from 239 pounds on the x-axis to the trend line. Next, we will draw a line from that point to the y-axis. This will qualitatively estimate our value. Observe this method below:

Now, lets predict this value quantitatively using the equation of the line:

Plug in 239 for the x-coordinate.

Solve

Round to two decimal places.

According to the data, we can predict that it would take a male 10.64 minutes for a 239 pound male to run a single mile.

Remember, we can also use this method to estimate the y-value of the data.

When data are presented using a scatter plot that is fitted with a trend line, we can calculate estimations based on the association between variables. Several conditions must be met before one can use a scatter plot to make estimates off of correlations.

First, the points must possess some type of relationship between one another. This relationship can be positive or negative. Positive relationships occur when data move upwards from the left side to the right side of the graph; however, when the data slopes downward the relationship is negative. Second, we must identify if the relationship is strong or weak. A strong correlation exists when the data is clustered closer together and the trend line. On the other hand, a weak correlation occurs when data is spread apart from each other and the trend line. After we have evaluated these characteristics of the graph, we can use the scatter plot to make predictions.

How do we make predictions? Predictions are made using several methods: qualitative and quantitative observations. One can qualitatively use the associations present in the graph to make estimates based on spread, clustering, and the trend line’s position. Spread between points in a given area can provide a range of values for a given coordinate, while clustering of plots in a given area can give an average value for a given coordinate. On the other hand, the trend line can be used to estimate points by drawing lines that intersect from each axis. Last, we can quantitatively estimate a point using the equation of the trend line and solving for either the x- or y-variable.

Let’s work with these methods and solve the question.

First let’s observe if we can make a prediction using the following data:

We can see that the data possesses a positive correlation: that is, as the runner’s weight increases then so does the time it takes them to run a mile. Also, we can see that the points are weakly to moderately clustered with one another and the trend line; therefore, we can use qualitative and quantitative means to estimate how fast a 155 pound male can run a mile.

Next, let’s make a qualitative estimate by drawing a line from 155 pounds on the x-axis to the trend line. Next, we will draw a line from that point to the y-axis. This will qualitatively estimate our value. Observe this method below:

Now, lets predict this value quantitatively using the equation of the line:

Plug in 155 for the x-coordinate.

Solve

Round to two decimal places.

According to the data, we can predict that it would take a male 9.37 minutes for a 155 pound male to run a single mile.

Remember, we can also use this method to estimate the y-value of the data.

When data are presented using a scatter plot that is fitted with a trend line, we can calculate estimations based on the association between variables. Several conditions must be met before one can use a scatter plot to make estimates off of correlations.

First, the points must possess some type of relationship between one another. This relationship can be positive or negative. Positive relationships occur when data move upwards from the left side to the right side of the graph; however, when the data slopes downward the relationship is negative. Second, we must identify if the relationship is strong or weak. A strong correlation exists when the data is clustered closer together and the trend line. On the other hand, a weak correlation occurs when data is spread apart from each other and the trend line. After we have evaluated these characteristics of the graph, we can use the scatter plot to make predictions.

How do we make predictions? Predictions are made using several methods: qualitative and quantitative observations. One can qualitatively use the associations present in the graph to make estimates based on spread, clustering, and the trend line’s position. Spread between points in a given area can provide a range of values for a given coordinate, while clustering of plots in a given area can give an average value for a given coordinate. On the other hand, the trend line can be used to estimate points by drawing lines that intersect from each axis. Last, we can quantitatively estimate a point using the equation of the trend line and solving for either the x- or y-variable.

Let’s work with these methods and solve the question.

First let’s observe if we can make a prediction using the following data:

We can see that the data possesses a positive correlation: that is, as the runner’s weight increases then so does the time it takes them to run a mile. Also, we can see that the points are weakly to moderately clustered with one another and the trend line; therefore, we can use qualitative and quantitative means to estimate how fast a 141 pound male can run a mile.

Next, let’s make a qualitative estimate by drawing a line from 141 pounds on the x-axis to the trend line. Next, we will draw a line from that point to the y-axis. This will qualitatively estimate our value. Observe this method below:

Now, lets predict this value quantitatively using the equation of the line:

Plug in 141 for the x-coordinate.

Solve

Round to two decimal places.

According to the data, we can predict that it would take a male 8.62 minutes for a 141 pound male to run a single mile.

Remember, we can also use this method to estimate the y-value of the data.

When data are presented using a scatter plot that is fitted with a trend line, we can calculate estimations based on the association between variables. Several conditions must be met before one can use a scatter plot to make estimates off of correlations.

First, the points must possess some type of relationship between one another. This relationship can be positive or negative. Positive relationships occur when data move upwards from the left side to the right side of the graph; however, when the data slopes downward the relationship is negative. Second, we must identify if the relationship is strong or weak. A strong correlation exists when the data is clustered closer together and the trend line. On the other hand, a weak correlation occurs when data is spread apart from each other and the trend line. After we have evaluated these characteristics of the graph, we can use the scatter plot to make predictions.

How do we make predictions? Predictions are made using several methods: qualitative and quantitative observations. One can qualitatively use the associations present in the graph to make estimates based on spread, clustering, and the trend line’s position. Spread between points in a given area can provide a range of values for a given coordinate, while clustering of plots in a given area can give an average value for a given coordinate. On the other hand, the trend line can be used to estimate points by drawing lines that intersect from each axis. Last, we can quantitatively estimate a point using the equation of the trend line and solving for either the x- or y-variable.

Let’s work with these methods and solve the question.

First let’s observe if we can make a prediction using the following data:

We can see that the data possesses a positive correlation: that is, as the runner’s weight increases then so does the time it takes them to run a mile. Also, we can see that the points are weakly to moderately clustered with one another and the trend line; therefore, we can use qualitative and quantitative means to estimate how fast a 164 pound male can run a mile.

Next, let’s make a qualitative estimate by drawing a line from 164 pounds on the x-axis to the trend line. Next, we will draw a line from that point to the y-axis. This will qualitatively estimate our value. Observe this method below:

Now, lets predict this value quantitatively using the equation of the line:

Plug in 164 for the x-coordinate.

Solve

y= 9.231

Round to two decimal places.

According to the data, we can predict that it would take a male 9.23 minutes for a 164 pound male to run a single mile.

Remember, we can also use this method to estimate the y-value of the data.

When data are presented using a scatter plot that is fitted with a trend line, we can calculate estimations based on the association between variables. Several conditions must be met before one can use a scatter plot to make estimates off of correlations.

First, the points must possess some type of relationship between one another. This relationship can be positive or negative. Positive relationships occur when data move upwards from the left side to the right side of the graph; however, when the data slopes downward the relationship is negative. Second, we must identify if the relationship is strong or weak. A strong correlation exists when the data is clustered closer together and the trend line. On the other hand, a weak correlation occurs when data is spread apart from each other and the trend line. After we have evaluated these characteristics of the graph, we can use the scatter plot to make predictions.

How do we make predictions? Predictions are made using several methods: qualitative and quantitative observations. One can qualitatively use the associations present in the graph to make estimates based on spread, clustering, and the trend line’s position. Spread between points in a given area can provide a range of values for a given coordinate, while clustering of plots in a given area can give an average value for a given coordinate. On the other hand, the trend line can be used to estimate points by drawing lines that intersect from each axis. Last, we can quantitatively estimate a point using the equation of the trend line and solving for either the x- or y-variable.

Let’s work with these methods and solve the question.

First let’s observe if we can make a prediction using the following data:

We can see that the data possesses a positive correlation: that is, as the runner’s weight increases then so does the time it takes them to run a mile. Also, we can see that the points are weakly to moderately clustered with one another and the trend line; therefore, we can use qualitative and quantitative means to estimate how fast a 211 pound male can run a mile.

Next, let’s make a qualitative estimate by drawing a line from 211 pounds on the x-axis to the trend line. Next, we will draw a line from that point to the y-axis. This will qualitatively estimate our value. Observe this method below:

Now, lets predict this value quantitatively using the equation of the line:

Plug in 211 for the x-coordinate.

Solve

Round to two decimal places.

According to the data, we can predict that it would take a male 8.59 minutes for a 211 pound male to run a single mile.

Remember, we can also use this method to estimate the y-value of the data.

When data are presented using a scatter plot that is fitted with a trend line, we can calculate estimations based on the association between variables. Several conditions must be met before one can use a scatter plot to make estimates off of correlations.

First, the points must possess some type of relationship between one another. This relationship can be positive or negative. Positive relationships occur when data move upwards from the left side to the right side of the graph; however, when the data slopes downward the relationship is negative. Second, we must identify if the relationship is strong or weak. A strong correlation exists when the data is clustered closer together and the trend line. On the other hand, a weak correlation occurs when data is spread apart from each other and the trend line. After we have evaluated these characteristics of the graph, we can use the scatter plot to make predictions.

How do we make predictions? Predictions are made using several methods: qualitative and quantitative observations. One can qualitatively use the associations present in the graph to make estimates based on spread, clustering, and the trend line’s position. Spread between points in a given area can provide a range of values for a given coordinate, while clustering of plots in a given area can give an average value for a given coordinate. On the other hand, the trend line can be used to estimate points by drawing lines that intersect from each axis. Last, we can quantitatively estimate a point using the equation of the trend line and solving for either the x- or y-variable.

Let’s work with these methods and solve the question.

First let’s observe if we can make a prediction using the following data:

We can see that the data possesses a positive correlation: that is, as the runner’s weight increases then so does the time it takes them to run a mile. Also, we can see that the points are weakly to moderately clustered with one another and the trend line; therefore, we can use qualitative and quantitative means to estimate how fast a 202 pound male can run a mile.

Next, let’s make a qualitative estimate by drawing a line from 202 pounds on the x-axis to the trend line. Next, we will draw a line from that point to the y-axis. This will qualitatively estimate our value. Observe this method below:

Now, lets predict this value quantitatively using the equation of the line:

Plug in 202 for the x-coordinate.

Solve

Round to two decimal places.

According to the data, we can predict that it would take a male 9.07 minutes for a 202 pound male to run a single mile.

Remember, we can also use this method to estimate the y-value of the data.

When data are presented using a scatter plot that is fitted with a trend line, we can calculate estimations based on the association between variables. Several conditions must be met before one can use a scatter plot to make estimates off of correlations.

First, the points must possess some type of relationship between one another. This relationship can be positive or negative. Positive relationships occur when data move upwards from the left side to the right side of the graph; however, when the data slopes downward the relationship is negative. Second, we must identify if the relationship is strong or weak. A strong correlation exists when the data is clustered closer together and the trend line. On the other hand, a weak correlation occurs when data is spread apart from each other and the trend line. After we have evaluated these characteristics of the graph, we can use the scatter plot to make predictions.

How do we make predictions? Predictions are made using several methods: qualitative and quantitative observations. One can qualitatively use the associations present in the graph to make estimates based on spread, clustering, and the trend line’s position. Spread between points in a given area can provide a range of values for a given coordinate, while clustering of plots in a given area can give an average value for a given coordinate. On the other hand, the trend line can be used to estimate points by drawing lines that intersect from each axis. Last, we can quantitatively estimate a point using the equation of the trend line and solving for either the x- or y-variable.

Let’s work with these methods and solve the question.

First let’s observe if we can make a prediction using the following data:

We can see that the data possesses a positive correlation: that is, as the runner’s weight increases then so does the time it takes them to run a mile. Also, we can see that the points are weakly to moderately clustered with one another and the trend line; therefore, we can use qualitative and quantitative means to estimate how fast a 174 pound male can run a mile.

Next, let’s make a qualitative estimate by drawing a line from 174 pounds on the x-axis to the trend line. Next, we will draw a line from that point to the y-axis. This will qualitatively estimate our value. Observe this method below:

Now, lets predict this value quantitatively using the equation of the line:

Plug in 174 for the x-coordinate.

Solve

Round to two decimal places.

According to the data, we can predict that it would take a male 9.42 minutes for a 174 pound male to run a single mile.

Remember, we can also use this method to estimate the y-value of the data.

When data are presented using a scatter plot that is fitted with a trend line, we can calculate estimations based on the association between variables. Several conditions must be met before one can use a scatter plot to make estimates off of correlations. 

First, the points must possess some type of relationship between one another. This relationship can be positive or negative. Positive relationships occur when data move upwards from the left side to the right side of the graph; however, when the data slopes downward the relationship is negative. Second, we must identify if the relationship is strong or weak. A strong correlation exists when the data is clustered closer together and the trend line. On the other hand, a weak correlation occurs when data is spread apart from each other and the trend line. After we have evaluated these characteristics of the graph, we can use the scatter plot to make predictions.

How do we make predictions? Predictions are made using several methods: qualitative and quantitative observations. One can qualitatively use the associations present in the graph to make estimates based on spread, clustering, and the trend line’s position. Spread between points in a given area can provide a range of values for a given coordinate, while clustering of plots in a given area can give an average value for a given coordinate. On the other hand, the trend line can be used to estimate points by drawing lines that intersect from each axis. Last, we can quantitatively estimate a point using the equation of the trend line and solving for either the x or y variable.

Let’s work with these methods and solve the question.

First let’s observe if we can make a prediction using the following data:

First, let’s observe if we can make a prediction using the following data:

We can see that the data possesses a positive correlation: that is, as the runner’s weight increases then so does the time it takes them to run a mile. Also, we can see that the points are weakly to moderately clustered with one another and the trend line; therefore, we can use qualitative and quantitative means to estimate how fast a 185 pound male can run a mile.

Next, let’s make a qualitative estimate by drawing a line from 185 pounds on the x-axis to the trend line. Next, we will draw a line from that point to the y-axis. This will qualitatively estimate our value. Observe this method below:

From this information, we can make the prediction that a male of this weight should be able to run a mile in just under ten minutes.

Now, lets predict this value quantitatively using the equation of the line:

Plug in 185 for the x-coordinate.

Solve.

Round to two decimal places.

According to the data, we can predict that it would take a male 9.71 minutes for a 185 pound male to run a single mile.

Remember, we can also use this method to estimate the y-value of the data.

When points are plotted in a linear regression model, trendlines or best-fit lines are used to make inferences and predictions about the data. There are several common trendline types: logarithmic, polynomial, exponential, power, and linear. Contrary to popular belief, a linear trendline is not always the best fit for every data set. In other words, we need to test the trendline to figure out whether or not it possesses strong associations of linearity between points. We can test this by graphing the plot’s residuals. 

What is meant by “residuals”? The residual of a point on a graph is calculated by subtracting the predicted y-value from its actual value. It is written using the following equation:

In this equation:

The actual values are represented by the points plotted on the graph, while the predicted values are represented by the trend line. The difference between each actual value and its predicted counterpart is the point's residual.

The question provided a table of the x- and y-values for the scatterplot. It also provided the equation of the linear trendline. Given this information, we can calculate the predicted y-values and the residuals of the scatterplot.

Let’s start by calculating the predicted y-values using the equation of the trendline and the x-values.

Lets start with the first x-value:

Now, calculate each predicted value for every x-coordinate in the scatter plot. Afterwards, calculate the residual for each point. For example,

Calculate the residuals for every point in the graph.

Now, we have calculated the predicted y-values and the residuals; therefore, we can create a graph of the residuals in the series. The graph will contain the residual values on the y-axis and the original x-values on the x-axis. 

Now, we can fit a trendline to the data. Notice that in this case the trendline is nearly horizontal. This indicates that there is a random spread in the residual data, which indicates that there is a linear correlation between points. The correct answer is "The graph is linear because the plot of the residuals possesses a random distribution." Now, we can determine a scatter plot's linearity using a graph of the plot's residuals.