Residuals 10th

How do you calculate a residual?

• Actual - Predicted

• Predicted - Actual

I predicted someone would lose 14 lbs, but they actually lost 12 lbs. Calculate the residual.

• 14 - 12 = 2

• 12 - 14 = -2

• 14 - 2 = 12

• 2 - 14 = -12

I predicted someone would score a 78% on their test, but they actually scored an 81%. Calculate the residual.

• 81 - 78 = 3

• 78 - 81 = -3

• 81 - 3 = 78

• 3 - 81 = -78

Interpret the residual 0

The actual point is...

• above the line, underestimate

• below the line, underestimate

• on the line

• above the line, underestimate

• below the line, overestimate

Answer explanation

Residual is the distance between the actual value and the predicted value.

If the residual is 0 that means the distance is 0, so the actual value is actually matches the predicted value (it's on the line!)

After performing a linear regression on a set of data, Jackie examined the residual plots. Which residual plot indicates that the linear model was a good fit?

• 
• 
• 
• 

Answer explanation

GOOD residual plots have RANDOM scatter.

They do NOT have any patterns or clusters of points

A linear regression was taken for a data set and produced the residual plot shown. Which statement is true about the residual plot?

• Graph A shows a non-linear fit because there is a distinct pattern to the data points

• Graph A shows a non-linear fit because there is not a distinct pattern to the data points

• Graph A shows linear fit because there is a distinct pattern to the data points

• Graph A shows linear fit because there is not a distinct pattern to the data points

Answer explanation

The residual plot of a linear scatter plot will have RANDOM scatter.

They do NOT have any patterns or clusters of points

A linear regression was taken that produced the following residual plot. The residual plot of a data set is shown. Which statement is true?

• Graph B shows non-linear fit because there is a distinct pattern to the data points

• Graph B shows non-linear fit because there is not a distinct pattern to the data points

• Graph B shows linear fit because there is a distinct pattern to the data points

• Graph B shows linear fit because there is not a distinct pattern to the data points

Answer explanation

The residual plot of a linear scatter plot will have RANDOM scatter.

They do NOT have any patterns or clusters of points

A residual plot compares the residual values (dependent variable) to the predicted values. Which of the following residual plots indicate that the regression model is a "good fit" to the data?

Select two residual plots.

• 
• 
• 
• 
• 

Answer explanation

The residual plot of a linear scatter plot will have RANDOM scatter.

They do NOT have any patterns or clusters of points

e

d

b

2

20

9

11

-18

-20

The regression equation y = 25x + 100 models the cost, y, of an event for x people.

The table shows what the party sizes actually paid. Complete the table with the predicted values and residuals.

e

f

g

h

d

c

overestimate

225

35

300

15

-15

underestimate

-35