1. If I want to predict one\'s college GPA based on their high school SAT scores

Question

1. If I want to predict one's college GPA based on their high school SAT scores with a regression equation, which is the predictor variable?                     GPA                SAT     (Highlight One).

2.   A regression equation predicts gross profit for a restaurant from the distance to the nearest major highway. The regression line follows:

                                  Y = -12X + 25,000

where X is the distance (in yards) from the highway, and Y is predicted gross profit in dollars.

2A. How much will the restaurant make each year if it is 500 yards from the highway.        

             3B. The correlation between distance from the highway and gross income is:

                                    Positive                      Negative         (circle one)         

            3C. What value does the equation give for slope?                          

            3D. At what point does the regression line cross the y-axis?       

Explanation / Answer

Question 1: As we are trying to predict GPA using the high school SAT scores, the predictor variable is clearly here the SAT and the predicted variable is the GPA.

Question 2: Y = -12X + 25,000

For a distance of 500 yards from the highway, that is X = 500, the predicted gross dollars would be:

Y = -12*500 + 25000 = 19,000

Therefore 19,000 is the predicted gross dollars.

Question 3:

3A. As the coefficient is negative for the variable X in the regression equation, the correlation between distance from the highway and gross income is negative.

3B. The slope of the equation is the coefficient of X that is -12.

3C. The regression equation crosses the y-axis at x=0, therefore y = 25000 is the point where the line crosses the y-axis.

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