Linear Models and Tables Review

The equation was ŷ = 10 + .9x where y is the final exam score and x is the score on the first test. Carla scored 95 on the first test. What is the predicted value of her score on the final exam?

• 95

• 85.5

• 90

• 95.5

The equation was ŷ = 10 + .9x where y is the final exam score and x is the score on the first test. Carla scored 95 on the first test, and on the final exam she scored a 98. What is the value of her residual?

• 3

• 2.5

• -2.5

• 0

A study of the fuel economy for various automobiles plotted the fuel consumption (in liters of gasoline used per 100 kilometers traveled) vs. speed (in kilometers per hour). Here is the residual plot from the least squares fit. What does the pattern of the residuals tell you about the linear model?

• There is nothing to conclude.

• The residual plot confirms the linearity of the fuel economy data.

• The residual plot contradicts the linearity of the data.

In regression, the residuals are which of the following?

• Factors unexplained by the data

• The difference between the observed responses and the values predicted by the regression line

• Data points which were recorded after the formal investigation was completed

• Possible models unexplored by the investigator

Which of the following statements is TRUE about correlation coefficients (r)?

• r values always have units

• r values can be greater than 1

• r values are used in the least squares regression line

• r values describe the direction and strength for linear models

Suppose the following information was collected, where X = diameter of tree trunk in inches, and Y = tree height in feet.

If the LSRL equation is ŷ = -3.6 + 3.1x, what is your estimate of the average height of all trees having a trunk diameter of 7 inches?

• 18.1

• 19.1

• 20.1

• 21.1

Least-squares regression lines are resistant to outliers and influential points, and will not change.

• True

• False

Correlation coefficients are resistant to outliers and influential points, and will not change.

• True

• False

If dataset A of (x,y) data has correlation coefficient r = 0.65, and a second dataset B has correlation r = –0.65, then

• The points in A exhibit a stronger linear association than B.

• The points in B exhibit a stronger linear association than A.

• Neither A nor B has a stronger linear association.

• You can’t tell which dataset has a stronger linear association without seeing the data or seeing the scatterplots.

A set of data relates the amount of annual salary raise and the performance rating. The least squares regression equation is ŷ = 1,400 + 2,000x where y is the estimated raise and x is the performance rating. Which of the following statements are correct? Select ALL that apply

• For each increase of one point in performance rating, the predicted raise will increase on average by $2,000.

• This equation produces predicted raises with an average error (sum of residuals) of 0.

• A rating of 0 will yield a predicted raise of $1,400.

• The correlation for the data is positive.