Fit Lines to Scatter Plots - 8th Grade Math
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What is a positive linear association in a scatter plot?
What is a positive linear association in a scatter plot?
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As $x$ increases, $y$ tends to increase. Both variables move in the same direction together.
As $x$ increases, $y$ tends to increase. Both variables move in the same direction together.
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What is the residual if actual $y=7$ and predicted $y=10$?
What is the residual if actual $y=7$ and predicted $y=10$?
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Residual $=7-10=-3$. Actual minus predicted gives negative when point is below line.
Residual $=7-10=-3$. Actual minus predicted gives negative when point is below line.
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What does it mean if points are widely scattered from a fitted line?
What does it mean if points are widely scattered from a fitted line?
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The linear model is a weak fit (weak linear association). Large scatter suggests the line poorly represents the data pattern.
The linear model is a weak fit (weak linear association). Large scatter suggests the line poorly represents the data pattern.
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What is a scatter plot used for when studying two quantitative variables?
What is a scatter plot used for when studying two quantitative variables?
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A graph that plots $(x,y)$ pairs to show the relationship between two variables. Visualizes how two quantitative variables relate to each other.
A graph that plots $(x,y)$ pairs to show the relationship between two variables. Visualizes how two quantitative variables relate to each other.
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What does a positive linear association look like in a scatter plot?
What does a positive linear association look like in a scatter plot?
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Points trend upward from left to right as $x$ increases. Shows a positive correlation between the variables.
Points trend upward from left to right as $x$ increases. Shows a positive correlation between the variables.
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Identify the slope sign if a fitted line goes down from left to right.
Identify the slope sign if a fitted line goes down from left to right.
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Negative slope, $m < 0$. Falling lines have negative slopes.
Negative slope, $m < 0$. Falling lines have negative slopes.
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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. Outliers can significantly affect the line of best fit.
A point far from the overall pattern of the data. Outliers can significantly affect the line of best fit.
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What is a line of best fit used for in a scatter plot?
What is a line of best fit used for in a scatter plot?
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To model the relationship and make predictions. The line helps estimate values and understand trends.
To model the relationship and make predictions. The line helps estimate values and understand trends.
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What is one key rule for informally drawing a line of best fit?
What is one key rule for informally drawing a line of best fit?
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Place about half the points above and half below the line. This balances the line through the data's center.
Place about half the points above and half below the line. This balances the line through the data's center.
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What does it mean when a scatter plot shows a linear association?
What does it mean when a scatter plot shows a linear association?
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Points trend around a straight line as $x$ changes. Linear association means data follows a straight-line pattern.
Points trend around a straight line as $x$ changes. Linear association means data follows a straight-line pattern.
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What does it mean if a scatter plot shows no linear association?
What does it mean if a scatter plot shows no linear association?
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There is no clear upward or downward linear trend. Points are scattered randomly without a linear pattern.
There is no clear upward or downward linear trend. Points are scattered randomly without a linear pattern.
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What is a negative linear association in a scatter plot?
What is a negative linear association in a scatter plot?
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As $x$ increases, $y$ tends to decrease. Variables move in opposite directions.
As $x$ increases, $y$ tends to decrease. Variables move in opposite directions.
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What is another key rule for informally drawing a line of best fit?
What is another key rule for informally drawing a line of best fit?
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Draw the line through the middle of the point cluster. The line should represent the overall trend of all points.
Draw the line through the middle of the point cluster. The line should represent the overall trend of all points.
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What does a strong linear association look like in a scatter plot?
What does a strong linear association look like in a scatter plot?
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Points lie close to a straight line. Little scatter means the linear model fits well.
Points lie close to a straight line. Little scatter means the linear model fits well.
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What does a weak linear association look like in a scatter plot?
What does a weak linear association look like in a scatter plot?
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Points are widely scattered around any line. Large scatter means the linear model fits poorly.
Points are widely scattered around any line. Large scatter means the linear model fits poorly.
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If a data point is at $(3,9)$ and the model predicts $y = 7$ at $x = 3$, what is the residual?
If a data point is at $(3,9)$ and the model predicts $y = 7$ at $x = 3$, what is the residual?
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Residual $= 2$. Residual = actual - predicted = $9 - 7 = 2$.
Residual $= 2$. Residual = actual - predicted = $9 - 7 = 2$.
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If a fitted line is $y = -3x + 10$, what is the predicted $y$ when $x = 2$?
If a fitted line is $y = -3x + 10$, what is the predicted $y$ when $x = 2$?
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$y = 4$. Substitute: $y = -3(2) + 10 = -6 + 10 = 4$.
$y = 4$. Substitute: $y = -3(2) + 10 = -6 + 10 = 4$.
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If a fitted line has equation $y = 2x + 1$, what is the predicted $y$ when $x = 4$?
If a fitted line has equation $y = 2x + 1$, what is the predicted $y$ when $x = 4$?
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$y = 9$. Substitute: $y = 2(4) + 1 = 8 + 1 = 9$.
$y = 9$. Substitute: $y = 2(4) + 1 = 8 + 1 = 9$.
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Find the slope of the line through $(1,8)$ and $(5,2)$.
Find the slope of the line through $(1,8)$ and $(5,2)$.
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$m = -\frac{3}{2}$. $m = \frac{2-8}{5-1} = \frac{-6}{4} = -\frac{3}{2}$.
$m = -\frac{3}{2}$. $m = \frac{2-8}{5-1} = \frac{-6}{4} = -\frac{3}{2}$.
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What does it mean to assess model fit informally on a scatter plot?
What does it mean to assess model fit informally on a scatter plot?
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Judge how close the points are to the fitted line. Closer points mean better model accuracy.
Judge how close the points are to the fitted line. Closer points mean better model accuracy.
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Which model fit is better: points tightly clustered or widely scattered around a line?
Which model fit is better: points tightly clustered or widely scattered around a line?
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Tightly clustered points indicate a better fit. Less scatter means more reliable predictions.
Tightly clustered points indicate a better fit. Less scatter means more reliable predictions.
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Identify the slope sign if a fitted line goes up from left to right.
Identify the slope sign if a fitted line goes up from left to right.
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Positive slope, $m > 0$. Rising lines have positive slopes.
Positive slope, $m > 0$. Rising lines have positive slopes.
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Find the $y$ value on the line $y=3x+2$ when $x=4$.
Find the $y$ value on the line $y=3x+2$ when $x=4$.
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$y=14$. Substitute $x=4$: $y=3(4)+2=12+2$.
$y=14$. Substitute $x=4$: $y=3(4)+2=12+2$.
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Which option is usually less reliable for a fitted line: interpolation or extrapolation?
Which option is usually less reliable for a fitted line: interpolation or extrapolation?
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Extrapolation. Predictions beyond data range are less certain.
Extrapolation. Predictions beyond data range are less certain.
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Identify the term for predicting $y$ for an $x$ value outside the data range using a fitted line.
Identify the term for predicting $y$ for an $x$ value outside the data range using a fitted line.
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Extrapolation. Making predictions beyond the observed data range.
Extrapolation. Making predictions beyond the observed data range.
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