Scatter Plots - PSAT Math
Card 1 of 30
Which prediction method is used when $x=12$ but the data only cover $x$ from $3$ to $10$?
Which prediction method is used when $x=12$ but the data only cover $x$ from $3$ to $10$?
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Extrapolation. $x=12$ exceeds the data range of $3$ to $10$.
Extrapolation. $x=12$ exceeds the data range of $3$ to $10$.
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Identify the residual for observed $(x,y)=(3,11)$ with prediction $
y=2x+4$.
Identify the residual for observed $(x,y)=(3,11)$ with prediction $ y=2x+4$.
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$1$. Residual = observed - predicted = $11-(2(3)+4)=11-10=1$.
$1$. Residual = observed - predicted = $11-(2(3)+4)=11-10=1$.
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For the model $y=-0.5x+10$, what is the predicted change in $y$ when $x$ increases by $4$?
For the model $y=-0.5x+10$, what is the predicted change in $y$ when $x$ increases by $4$?
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$
y$ changes by $-2$. Change is $(-0.5)(4)=-2$.
$ y$ changes by $-2$. Change is $(-0.5)(4)=-2$.
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Use $y=2x+5$ to predict $y$ when $x=4$.
Use $y=2x+5$ to predict $y$ when $x=4$.
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$y=13$. Substitute: $y=2(4)+5=8+5=13$.
$y=13$. Substitute: $y=2(4)+5=8+5=13$.
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Find $b$ for $y=mx+b$ if the line has $m=3$ and passes through $(2,7)$.
Find $b$ for $y=mx+b$ if the line has $m=3$ and passes through $(2,7)$.
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$b=1$. Substitute: $7=3(2)+b$, so $b=7-6=1$.
$b=1$. Substitute: $7=3(2)+b$, so $b=7-6=1$.
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Find $m$ for a best-fit line through $(2,5)$ and $(6,13)$ using $m= rac{y_2-y_1}{x_2-x_1}$.
Find $m$ for a best-fit line through $(2,5)$ and $(6,13)$ using $m= rac{y_2-y_1}{x_2-x_1}$.
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$m=2$. $m= rac{13-5}{6-2}= rac{8}{4}=2$.
$m=2$. $m= rac{13-5}{6-2}= rac{8}{4}=2$.
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Which prediction method is used when $x=7$ and the data cover $x$ from $3$ to $10$?
Which prediction method is used when $x=7$ and the data cover $x$ from $3$ to $10$?
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Interpolation. $x=7$ falls within the data range of $3$ to $10$.
Interpolation. $x=7$ falls within the data range of $3$ to $10$.
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Identify the correlation type if points trend upward from left to right.
Identify the correlation type if points trend upward from left to right.
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Positive correlation. Upward trend indicates positive correlation.
Positive correlation. Upward trend indicates positive correlation.
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Identify the correlation type if points trend downward from left to right.
Identify the correlation type if points trend downward from left to right.
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Negative correlation. Downward trend indicates negative correlation.
Negative correlation. Downward trend indicates negative correlation.
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What is extrapolation when using a scatter plot model?
What is extrapolation when using a scatter plot model?
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Predicting outside the range of observed $x$-values. Extends predictions beyond the data's domain.
Predicting outside the range of observed $x$-values. Extends predictions beyond the data's domain.
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What is interpolation when using a scatter plot model?
What is interpolation when using a scatter plot model?
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Predicting within the range of observed $x$-values. Uses the model within the data's domain.
Predicting within the range of observed $x$-values. Uses the model within the data's domain.
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What is the meaning of the $y$-intercept $b$ in a best-fit line $y=mx+b$?
What is the meaning of the $y$-intercept $b$ in a best-fit line $y=mx+b$?
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The predicted value of $y$ when $x=0$. The $y$-intercept is where the line crosses the $y$-axis.
The predicted value of $y$ when $x=0$. The $y$-intercept is where the line crosses the $y$-axis.
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What is the slope meaning in a best-fit line $y=mx+b$ on a scatter plot?
What is the slope meaning in a best-fit line $y=mx+b$ on a scatter plot?
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The predicted change in $y$ for a $1$-unit increase in $x$. Slope shows rate of change between variables.
The predicted change in $y$ for a $1$-unit increase in $x$. Slope shows rate of change between variables.
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What does it mean if points lie close to a straight line in a scatter plot?
What does it mean if points lie close to a straight line in a scatter plot?
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The association is strong (little scatter around a line). Points cluster tightly around a linear pattern.
The association is strong (little scatter around a line). Points cluster tightly around a linear pattern.
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What does a negative association in a scatter plot mean as $x$ increases?
What does a negative association in a scatter plot mean as $x$ increases?
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$y$ tends to decrease as $x$ increases. Points trend downward from left to right in negative associations.
$y$ tends to decrease as $x$ increases. Points trend downward from left to right in negative associations.
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What does a positive association in a scatter plot mean as $x$ increases?
What does a positive association in a scatter plot mean as $x$ increases?
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$y$ tends to increase as $x$ increases. Points trend upward from left to right in positive associations.
$y$ tends to increase as $x$ increases. Points trend upward from left to right in positive associations.
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What does the $y$-intercept of a best-fit line represent in context?
What does the $y$-intercept of a best-fit line represent in context?
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The predicted value of $y$ when $x=0$. Shows the starting value when the independent variable is zero.
The predicted value of $y$ when $x=0$. Shows the starting value when the independent variable is zero.
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Identify the predicted $y$ when the model is $y = -3x + 10$ and $x = 2$.
Identify the predicted $y$ when the model is $y = -3x + 10$ and $x = 2$.
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$4$. Substitute: $y = -3(2) + 10 = -6 + 10 = 4$.
$4$. Substitute: $y = -3(2) + 10 = -6 + 10 = 4$.
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Find the equation of the line through $(1,4)$ with slope $m=3$ in $y=mx+b$ form.
Find the equation of the line through $(1,4)$ with slope $m=3$ in $y=mx+b$ form.
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$y=3x+1$. Substitute $(1,4)$: $4=3(1)+b$, so $b=1$.
$y=3x+1$. Substitute $(1,4)$: $4=3(1)+b$, so $b=1$.
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Identify the $y$-intercept of the line $y=0.8x-12$.
Identify the $y$-intercept of the line $y=0.8x-12$.
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$-12$. The constant term when the equation is in $y=mx+b$ form.
$-12$. The constant term when the equation is in $y=mx+b$ form.
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What is the slope formula for a line of best fit through $(x_1,y_1)$ and $(x_2,y_2)$?
What is the slope formula for a line of best fit through $(x_1,y_1)$ and $(x_2,y_2)$?
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$m= rac{y_2-y_1}{x_2-x_1}$. Rise over run between two points on a line.
$m= rac{y_2-y_1}{x_2-x_1}$. Rise over run between two points on a line.
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What is a line of best fit in a scatter plot?
What is a line of best fit in a scatter plot?
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A line that approximates the overall trend of the points. Minimizes distances to all points to show the trend.
A line that approximates the overall trend of the points. Minimizes distances to all points to show the trend.
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What is an outlier in a scatter plot?
What is an outlier in a scatter plot?
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A point far from the overall pattern of the data. Deviates significantly from where other points cluster.
A point far from the overall pattern of the data. Deviates significantly from where other points cluster.
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What does it mean if a scatter plot shows no correlation?
What does it mean if a scatter plot shows no correlation?
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There is no clear trend relating $x$ to $y$. Points are scattered randomly without a linear pattern.
There is no clear trend relating $x$ to $y$. Points are scattered randomly without a linear pattern.
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Which option describes negative correlation in a scatter plot?
Which option describes negative correlation in a scatter plot?
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As $x$ increases, $y$ tends to decrease. Points trend downward from left to right on the graph.
As $x$ increases, $y$ tends to decrease. Points trend downward from left to right on the graph.
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What is the point-slope form of a line used with a best-fit slope $m$ through $(x_1,y_1)$?
What is the point-slope form of a line used with a best-fit slope $m$ through $(x_1,y_1)$?
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$y-y_1=m(x-x_1)$. Rearranges to find the line equation from a point and slope.
$y-y_1=m(x-x_1)$. Rearranges to find the line equation from a point and slope.
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Which option describes positive correlation in a scatter plot?
Which option describes positive correlation in a scatter plot?
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As $x$ increases, $y$ tends to increase. Points trend upward from left to right on the graph.
As $x$ increases, $y$ tends to increase. Points trend upward from left to right on the graph.
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What does the term correlation describe in a scatter plot?
What does the term correlation describe in a scatter plot?
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The direction and strength of association between $x$ and $y$. Measures how closely variables move together in a linear pattern.
The direction and strength of association between $x$ and $y$. Measures how closely variables move together in a linear pattern.
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What is a scatter plot used to display about two quantitative variables?
What is a scatter plot used to display about two quantitative variables?
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A set of paired data points $(x, y)$ showing their relationship. Visualizes how two variables relate by plotting coordinate pairs.
A set of paired data points $(x, y)$ showing their relationship. Visualizes how two variables relate by plotting coordinate pairs.
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Identify the slope of the line through the points $(2,5)$ and $(6,1)$.
Identify the slope of the line through the points $(2,5)$ and $(6,1)$.
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$-1$. Apply slope formula: $m= rac{1-5}{6-2}= rac{-4}{4}=-1$.
$-1$. Apply slope formula: $m= rac{1-5}{6-2}= rac{-4}{4}=-1$.
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