AP Stats Benchmark Review

Which of the following statements about a linear regression model is true?

I. The sum of the residuals is always zero

II. If r²=0, the regression line is a horizontal line.

III. No pattern in the residual plot is an indication that a nonlinear model will show a better fit to the data than a straight-line regression model.

• I and II only

• I only

• I and III only

• II and III only

• I, II, and III

In a statistics course, a linear regression equation was computed to predict the final exam score based on the score on the first test of the term. The equation was y=25+0.7x where y is the final exam score and x is the score on the first test. George scored 80 on the first test. On the final exam George scored 85. What is the value of his residual?

• -4

• 4

• 4.5

• 5

• 81

What is the effect on the correlation between two variables (x, y) if each x value is cut in half and 0.04 is subtracted from each y value?

• The correlation is cut in half.

• The correlation is unchanged.

• The correlation is decreased by 0.04.

• The correlation is decreased by 0.0016.

• The correlation is doubled.

Which of the following statements about correlation, r, are true?

I. When r = 0 , there is no linear relationship between the variables.

II. When r = 0.75, then 75% of the variables are closely related

III. When r = 1, there is a perfect cause and effect relationship between the variables.

• I only

• II only

• III only

• I and III only

• I, II, and III

Which of the following best describes the correlation between two variables if r = 0.987?

• positive and strong

• negative and weak

• positive and weak

• negative and strong

• no correlation

The correlation coefficient is

• always equal to the slope of the regression line

• a positive number that measures the goodness of fit

• never equal to zero

• A number between -1 and +1 that measures the strength and direction of the linear relationship between two variables

• the fraction of the variation in the values of y that is explained by the least-squares regression of y on x.

The residual plot below came from data which plotted grade at midterm against grade on final exam. A linear regression line was calculated. Which conclusion could be reached by analyzing the residual plot?

• Students did better on the final exam than they did on the midterm.

• There is evidence that a linear model is appropriate.

• An exponential curve could be used to predict final grade given midterm grade.

• There exists unequal variance throughout the model.

• There is no pattern evident in the residual plot.

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• 
• 
• 
• 

A student was interested in the relationship between weight of a car and gas consumption measured in mpg. He selected sixteen different automobiles and recorded their weights along with their advertised mpg. The regression equation and regression plot are shown above.

What affect would the addition of the point (4,300 lbs, 15.63 mpg) have on the value of r²?

• It will increase r² because it is an influential point which lies on the least squares line.

• It will have no effect on r² because it lies on the line.

• It will decrease r² because it is an outlier

• It will increase r² because every additional point will increase the percent variation in y due to the relationship with the lease squares line.

The equation of the least squares regression line for a set of points in a scatterplot is given above. The point (5, 7) is one point on this scatterplot. Which of the following is the residual for the point (5, 7)?

• 6.25

• 4.05

• 0.71

• 0.75

• 7.87