[answered] 1. Use the following data to answer the questions below: Gr

Use the following data to answer the questions below:

Grade Point Average and Family Income

 Student Income (\$000?s) (X) GPA (Y) A 21 4.0 B 15 3.0 C 15 3.5 D 9 2.0 E 12 3.0 F 18 3.5 G 6 2.5 H 12 2.5

1. Use the following data to answer the questions below:

Grade Point Average and Family Income

Student

A

B

C

D

E

F

G

H Income (\$000?s)

(X)

21

15

15

9

12

18

6

12 GPA

(Y)

4.0

3.0

3.5

2.0

3.0

3.5

2.5

2.5 a) Draw a scatter diagram. b) Does the relationship look linear? c) Using the following values, interpret the slope (b=0.12) and intercept (a=1.36) in

plain English. Class 11/12 Homework Assignment

Page 1 of 4 d) If a family has an income of \$10,000 what GPA would you expect the student to

have? e) Using a value of r=0.88, calculate the Coefficient of Determination (R 2). f) Interpret the Coefficient of Determination (R 2) in the context of the problem. Class 11/12 Homework Assignment

Page 2 of 4 2. You are a consultant on a project that looks at the difficulties of closing down a

business across countries. The table below provides information for a random sample

of countries. It lists the amount of time in years needed to close a business and the

recovery rate on the initial investment.

Country

Azerbaijan

Colombia

Finland

Israel

Czech Republic

Turkey

India

Iceland

United Kingdom

United States

Brazil Time in Years Recovery rate (cents on the dollar)

2.7

33

3

55.2

0.9

89.1

4

42.8

9.2

17.9

5.9

7.2

10

12.8

1

81.7

1

85.3

2

76.3

4

24.3

10

0.5 Developed Nation

No

No

Yes

Yes

No

No

No

No

Yes

Yes

No

No (Note: The statistics are from the World Bank Doing Business Report) (a) Using a value of R = -0.8692, calculate the R2. Interpret the R2 in words. Class 11/12 Homework Assignment

Page 3 of 4 3. The weight of a car is an important determinant of its fuel efficiency. Below is a

scatterplot of the relationship between vehicle weight in tons (WT_TONS) against fuel

efficiency (Miles per Gallon), based upon an analysis of 398 different models of cars.

Also included is output from the bivariate regression in which miles per gallon is

predicted by WT_TONS: a) Write the regression equation that describes the relationship between vehicle weight

and fuel efficiency. b) Interpret the coefficient on ?WT_TONS?, in your equation above, in plain English. c) Draw the regression line onto the figure. (It may be helpful to start by putting in two

points that you know are on the line). Class 11/12 Homework Assignment

Page 4 of 4

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