Exercise 22. In the lecture notes we use a regression line of the form y = a + 3x to predict y from x. Instead, we could have used x = y + dy to predict æ from y. Is this the same model in a different form, or a different model?

Management proposed the following regression model to predict sales at a fast-food outlet. y = Bo + B,x1 + B2X2 + B3X3 + E where X1 = number of competitors within one mile X2 = population within one mile (1,000s) J1 if drive-up window present 0 otherwise y = sales ($1,000s). X3 = The following estimated regression equation was developed after 20 outlets were surveyed. ŷ = 10.5 – 4.2x, + 6.8x2 + 15.9x3 (a) What is the expected amount of sales (in dollars) attributable to the drive-up window? $ (b) Predict sales (in dollars) for a store with three competitors within one mile, a population of 8,000 within one mile, and a drive-up window. 24 (c) Predict sales (in dollars) for a store with one competitor within one mile, a population of 3,000 within one mile, and no drive-up window. $4

Data on the average Scholastic Aptitude Test verbal and mathematics scores for high school seniors in each of the fifty states show a strong straight-line association. The regression line for predicting a state’s average math score (y) from the average verbal score (x) is y = 1.03x – 15 a. The average SAT verbal score in New York was 433. Use the regression line to predict New York’s average math score.

The equation used to predict college GPA (range 0-4.0) is y= 0.17 +0.52x, +0.002x,, where x, is high school GPA (range 0-4.0) and X2 is college board score (range 200-800). Use the multiple regression equation to predict college GPA for a high school GPA of 3.1 and a college board score of 600.

A college bookstore must order books two months before each semester starts. They believe that the number of books that will ultimately be sold for any particular course is related to the number of students registered for the course when the books are ordered. They would like to develop a linear regression equation to help plan how many books to order. From past records, the bookstore obtains the number of students registered, X, and the number of books actually sold for a course, Y, for 12 different semesters. These data are below. Show the complete table for your solutions.   At a .01 level of significance is there sufficient evidence to conclude that the number of books sold is related to the number of registered students in a straight-line manner? Calculate df:Indicate whether it is a one-tail or two-tail test:Use the table for PEARSON'S CORRELATION COEFFICIENT r (Critical Values):Make a Decision by comparing critical r with the computer Pearson Correlation Coefficient:

Given the regression model Y=15+7X what will be the value of Y when X is 0?

For the regression equation, Ŷ = –2X + 6, what can be determined about the correlation between X and Y?

The number of students in a school chorus has increased since the school first opened 6 years ago. The linear regression equation describing the change is y = 14x + 17, where a represents the year and y represents the number of students. a. Complete the table to determine the residuals for the numberr of students. Then create a residual graph with the X's on the x axis and residuals on the y-axis. Predicted Number of Residual Value Year Number of Students Students 22 26 40 59 78 4 83 Residual Plot 6 -4 3 2 -2 -1 -1 916 esc DII F4 FS F7 FB @ %23 2$ 1 2 3. 4. 7 8. Q W E R T Y tab S D F G caps lock Z C V N shift B A

= In a statistics course, a linear regression equation was computed to predict the final-exam score from the score on the first test. The equation as y 10+ 0.75x where y is the final-exam score and x is the score on the first test. Parvez scored 80 on the first test. What is the predicted value of the Parvez's score on the final exam? Parvez scored 60 on the final exam. What is the value of the residual?

The table below shows the amounts of crude oil (in thousands of barrels per day) produced by a country and the amounts of crude oil (in thousands of barrels per day) imported by a country, for the last 7 years. Construct and interpret a 98% prediction interval for the amount of oil imported by the country and the amount of oil produced by the country is 5,483 thousand barrels per day. The equation of the regression line is y = -1.194x + 16,234.906