Fit Lines to Scatter Plots - 8th Grade Math

Residual $=7-10=-3$. Actual minus predicted gives negative when point is below line.

The linear model is a weak fit (weak linear association). Large scatter suggests the line poorly represents the data pattern.

A graph that plots $(x,y)$ pairs to show the relationship between two variables. Visualizes how two quantitative variables relate to each other.

Points trend upward from left to right as $x$ increases. Shows a positive correlation between the variables.

Negative slope, $m < 0$. Falling lines have negative slopes.

A point far from the overall pattern of the data. Outliers can significantly affect the line of best fit.

To model the relationship and make predictions. The line helps estimate values and understand trends.

Place about half the points above and half below the line. This balances the line through the data's center.

Points trend around a straight line as $x$ changes. Linear association means data follows a straight-line pattern.

There is no clear upward or downward linear trend. Points are scattered randomly without a linear pattern.

As $x$ increases, $y$ tends to decrease. Variables move in opposite directions.

Draw the line through the middle of the point cluster. The line should represent the overall trend of all points.

Points lie close to a straight line. Little scatter means the linear model fits well.

Points are widely scattered around any line. Large scatter means the linear model fits poorly.

Residual $= 2$. Residual = actual - predicted = $9 - 7 = 2$.

$y = 4$. Substitute: $y = -3(2) + 10 = -6 + 10 = 4$.

$y = 9$. Substitute: $y = 2(4) + 1 = 8 + 1 = 9$.

$m = -\frac{3}{2}$. $m = \frac{2-8}{5-1} = \frac{-6}{4} = -\frac{3}{2}$.

Judge how close the points are to the fitted line. Closer points mean better model accuracy.

Tightly clustered points indicate a better fit. Less scatter means more reliable predictions.

Positive slope, $m > 0$. Rising lines have positive slopes.

$y=14$. Substitute $x=4$: $y=3(4)+2=12+2$.

Extrapolation. Predictions beyond data range are less certain.

Extrapolation. Making predictions beyond the observed data range.

$16-20=-4$. Residual = actual - predicted value.

$y=-2$. Substitute $x=6$: $y=-2(6)+10=-12+10$.

Points trend downward from left to right as $x$ increases. Shows a negative correlation between the variables.

The linear model is a poor fit (weak linear association). Points deviate significantly from the line.

$rac{1-9}{5-1}=-2$. Use slope formula: $rac{y_2-y_1}{x_2-x_1}$.