P11.1011 Statistical Methods for Public, Nonprofit, and Health Management Student's name: Mailbox number: Homework Class 11 and 12 combined 1. Use the following data to answer the questions below. Note that b=0.12 and a=1.36. Grade Point Average and Family Income a) Draw a scatter diagram. b) Does the relationship look linear? Class 11/12 Homework Assignment Page 1 of5 c) Interpret the slope (b=0.12) in plain English. 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 (R2). f) Interpret the Coefficient of Determination (R2) in the context of the problem. Class 11/12 Homework Assignment Page 2 of5 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 Time in Years Recovery rate (cents on the dollar] Developed Nation Azerbaijan 2.7 33 1\\o Colombia 3 55.2 1\\o *7inland 0.9 89.1 Yes srael 4 42.8 Yes Czech Republic 9.2 17.9 1\\o Turkey 5.9 7.2 1\\o ndia 10 12.8 1\\o celand 1 81.7 1\\o Jnited Kingdom 1 85.3 Yes Jnited States 2 76.3 Yes Bangladesh 4 24.3 1\\o Brazil 10 0.5 1\\o (Note: The statistics are from the World Bank Doing Business Report) (a) Using a value of R = -O.8692, calculate the R2. Interpret the R2 in words. Class 11/12 Homework Assignment Page 3 of5 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 pounds (weight) against fuel efficiency (mpg, 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 weight: 2 2 2,000 3,000 4,000 5,000 Weight (Ibs.) Mileage (mpg) Fitted values . regress mpg weight Source SS df MS Number of obs 74 F (1, 72) 134. 62 Model 1591. 9902 1 1591. 9902 Prob > F 0. 0000 Residual 851. 469256 72 11. 8259619 R-squared 0 . 6515 Adj R-squared 0 . 6467 Total 2443 . 45946 73 33.4720474 Root MSE 3 . 4389 mpg Coef. Std. Err. t P>/ t/ [95% Conf. Interval] weight -. 0060087 . 0005179 -11. 60 0. 000 -. 0070411 - . 0049763 _cons 39 . 44028 1. 614003 24.44 0. 000 36. 22283 42 . 65774 a) Write the regression equation that describes the relationship between vehicle weight and fuel efficiency. (Question continued on next page) Class 11/12 Homework Assignment Page 4 of 5b) Interpret the coefficient on \"WEIGHT", in your equation above, in plain English. Class 11/12 Homework Assignment Page 5 of5