s. (6 points) The Economist published economic data for 15 industrialized nation
ID: 3350514 • Letter: S
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s. (6 points) The Economist published economic data for 15 industrialized nations. Included were the p change in gross domestic product (GDP). industrial production (IP), consumer prices (CP), and producer prhice (PP), and the unemployment rate (UNEMP). After all linear regression modeling assumptions the multiple linear regression model to predict GDP from IP, CP. PP were met, a fit of and UNEMP yields the following results: Predictor Constant IP UNEMP CP CoefSE Cof 18957.42180 17326 .041962 .17918 0.045895 0.11365 2.82 0.01 4.130.002 .90 0.003 1.550.15 0.17591 0.18393 0.068808-2.67 0.023 Predict the percent change in GDP for a country with IP-05, UNEMP= 6, CP-20 and PP-41 a. b. If two countries differ in industrial production by 1%, by how much would you predict their percent change in GDP to differ, other things being equal? The CP and PP are both measures of the inflation rate. Which one is more useful in predicting GPD? Briefly explain your answer. c. 9. (6 points) A sample of 87 glass sheets has a mean thickness of 4.20mm with a standard deviation of 0.10mm. a. Find a 98% confidence interval for the population mean thickness. How many glass sheets must be sampled so that a 98% confidence interval will specify the mean to within ± 0.01 5?Explanation / Answer
8.(a) The regression equation is: GDP = y = 1.18957 + (0.17326 * IP) + (0.17918 * UNEMP) + (0.17591 * CP) - (0.18393 * PP).
Putting IP = 0.5, UNEMP = 6, CP = 2.0 and PP = 4.1, we get y = GDP = 1.94898% change = 1.95% change (approx.)
(b) From the regression coefficient of IP, which is 0.17326, we can say that if IP changes by 1%, the GDP will differ by 0.17% (approx.).
(c) PP is more useful in predicting GDP because it has a p-value which is less than 0.05, in contrast to CP, whose p-value is greater than 0.05. This tells us that PP is a significant predictor variable in the regression equation, whereas CP is not.
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