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All Common Core: High School - Statistics and Probability Resources

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Flashcards: Interpret Slope and Intercept of a Linear Model: CCSS.Math.Content.HSS-ID.C.7

A professor conducts a study on the relationship between sleep and academic performance by asking his 420 students how many hours of sleep they missed while studying for the class final.

The regression output is as follows:

$\widehat{Points\ on\ Final}=698.8-2.28\times Sleep\ Hours\ Missed$

Which of the following statements is TRUE?

The average score on the final is 696.52 points.

The average score on the final is 698.8 points.

For every additional hour of sleep missed, the number of points scored on the final decreases by 2.28 points.

Sleep has no effect on academic performance.

The regression equation itself proves that the results are statistically significant.

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Flashcards: Interpret Slope and Intercept of a Linear Model: CCSS.Math.Content.HSS-ID.C.7

A professor conducts a study on the relationship between sleep and academic performance by asking his 420 students how many hours of sleep they missed while studying for the class final.

The regression output is as follows:

$\widehat{Points\ on\ Final}=698.8-2.28\times Sleep\ Hours\ Missed$

Which of the following statements is TRUE?

Your answer:

The average score on the final is 696.52 points.

Your answer:

The average score on the final is 698.8 points.

Your answer:

Sleep has no effect on academic performance.

Your answer:

The regression equation itself proves that the results are statistically significant.

Correct answer:

For every additional hour of sleep missed, the number of points scored on the final decreases by 2.28 points.

Explanation:

Flashcards: Interpret Slope and Intercept of a Linear Model: CCSS.Math.Content.HSS-ID.C.7

Identify the slope of the following line:

Y x 1

$m=\frac{1}{2}$

m=1

$m=\frac{2}{5}$

$m=\frac{1}{5}$

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Flashcards: Interpret Slope and Intercept of a Linear Model: CCSS.Math.Content.HSS-ID.C.7

Identify the slope of the following line:

Y x 1

Your answer:

$m=\frac{1}{2}$

Your answer:

$m=\frac{2}{5}$

Your answer:

$m=\frac{1}{5}$

Correct answer:

m=1

Explanation:

This question asks us to analyze the constituent components of a linear equation written in the slope intercept formula:

y=mx+b

This formula provides information about two key parts of a line: the slope and y-intercept.

$m=\textup{slope}$

The slope is commonly defined as rise over run. In other words it is the change in y-values across points divided by the change in x-values. It is calculated using the following formula:

$m=\frac{\Delta y}{\Delta x}$

$m=\frac{y_{2}-y_{y1}}{x_{2}-x_{1}}$

In this formula, the x and y-values come from two points from the line written in the following format:

(x,y)

It is important to note that slopes can be positive or negative. A positive slope moves upward from left to right while a negative slope moves downward.

Now, lets solve the problem. We will start by identifying two points on the line. Lets observe the point where the line crosses the x-axis and the point to where it crosses , positive five, on the x-axis.

These two points are:

$(-1, 0) \textup{ and }(5,6)$

Now, substitute these numbers into the slope formula.

$m=\frac{y_{2}-y_{y1}}{x_{2}-x_{1}}$

$m=\frac{6-0}{5-(-1)}$

$m=\frac{6}{6}$

m=1

The slope is positive because the line moves upward from left to right.

We find that the slope of the equation is one. We can also calculate the slope by using the traditional "rise over run" definition. If we count blocks on the graph we can see that for every six blocks that it "rises," it "runs" six blocks. In other words, the slope increases one block in the x-direction as it increases one block in the y-direction; therefore, the slope is one (see figure below).

Y x 1 slope

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All Common Core: High School - Statistics and Probability Resources

Flashcards: Interpret Slope and Intercept of a Linear Model: CCSS.Math.Content.HSS-ID.C.7

Flashcards: Interpret Slope and Intercept of a Linear Model: CCSS.Math.Content.HSS-ID.C.7

Flashcards: Interpret Slope and Intercept of a Linear Model: CCSS.Math.Content.HSS-ID.C.7

Flashcards: Interpret Slope and Intercept of a Linear Model: CCSS.Math.Content.HSS-ID.C.7

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