Regression Analysis of Production Costs in Automotive Industry

Exam 3 Instructor: Lu Liu Name: Class: MKT 435 ID: Part I (Short Answer): Each question worth 25 pts, the total is 50 pts. Page 1

Page 2 1) The regression results below represent the cost of factory production of automobile headlights for Toyota cars at one factory. Answer the following questions. (25 points) Regression Statistics Multiple R 0.749591807 R Square 0.561887878 Adjusted R Square 0.474265453 Standard Error 42861.35168 Observations 19 Coefficients Standard Error t Stat P-value Intercept 1081275.15 77244.49507 13.99808684 5.13021E-10 Corolla 19.2850886 13.03175458 1.479853575 0.249607524 Camry 20.72528603 7.689781205 2.695172396 0.101661886 Avalon 33.23260325 32.71775573 1.015736028 0.025859682 1.1: What does the R Square mean in this specific example? (5 points) 1.2: Interpret the intercept and all coefficients. What do they mean in this specific example? (20 points, please interpret all the 4 parameters, each one worth 5 pts) 2): The results below represent the correlation matrix of the number of vehicles manufactured for Corolla, Camry, Avalon automobiles and the overall production cost of the factory. Answer the following questions. (25 points) 2.1 Which two cars (production quantities) have the strongest correlation to each other (largest magnitude)? What is the correlation? (5 points)

Part II (Calculations): Show the process and result. Each question worth 25 pts, the total is 50 pts. Consider the regression model defined for the per capita sales of brand X in a sales territory in the USA: Y = β 0 + β 1 D 1 + β 2 D 2 + β 3 D 3 + β 4 X + β 5 D 1 X + β 6 D 2 X + β 7 D 3 X where: Y=per capita dollar sales of Brand X in 2010 in a territory (sales); D 1 =1 if the territory is from Eastern USA, else 0; D 2 =1 if the territory is from Western USA, else 0; D 3 =1 if the territory is from Southern USA, else 0; X=per capita dollar advertising in the territory. 3.1(10pts) Write the regression equation separately for the four categories (Eastern, Western, Southern, Other). 3.2Express each of the following hypothesis in terms of the parameters of the regression model. 3.2.1(5pts) The marginal effect of advertising on sales is equal for Eastern, Western and Southern territories. 3.2.2(5pts) The marginal effect of advertising on sales is zero for Western territories. 3.2.3(5pts) The regression line is the same (both intercept and slope) for Eastern and Southern territories. Page 3

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A researcher has collected a random sample of 100 US adults in 2016 and recorded which state the person is from, and whether the person is satisfied with the work of President Obama, the results are as follows: State Number of Respondents that are satisfied with the work of President Obama Number of Respondents that are not satisfied with the work of President Obama California 10 20 New York 10 10 Ohio 20 10 Montana 15 5 Suppose you are asked to test at a 95% level of confidence that an equal proportion of adults in the four states are satisfied with the work of President Obama, show your work. (25pts) Page 4

Exam 3 MKT435

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