34. Refer to Exercise 3 where we are trying to link mortgage interest rate (x) to home sales (y). The estimated regression equation there was ŷ = 90 − 4x. 1. Show the 90% confidence interval estimate of the “population” intercept, α. Interpret your interval. 2. Show the 90% confidence interval estimate of the “population” slope, β. Interpret your interval. 37. Refer to Exercise 9 where we were trying to link customer waiting time (x) to customer satisfaction (y). The boundaries for a 95% confidence interval estimate of the “population” slope here are −6.271 and 2.671. Could we reasonably believe that the “population” slope, β, is actually 0? 4.2? −2.5? 40. Refer to Exercise 3 where we are trying to link mortgage interest rate (x) to home sales (y). The estimated regression equation there was ŷ = 90 − 4x. Can we reject the null hypothesis that the population slope, β, is 0 at the 1% significance level? Explain the implications of your answer. 44. Refer to Exercise 9 where we are trying to link customer waiting time (x) to customer satisfaction (y). The estimated regression equation turned out to be ŷ = 126 − 1.8x. Is the sample slope (b = −1.8) significantly different from 0 at the 5% significance level? Explain the implications of your answer. 51. Refer to Exercise 4, where we are trying to link average hourly wage (x) to employee turnover (y). The estimated regression equation turned out to be ŷ = 139.2 − 6.7x. Show the 95% confidence interval estimate of the expected turnover rate for the population of all companies with an average hourly wage of $15. 57. Refer to Exercise 4, where we are trying to link average hourly wage (x) to employee turnover (y). The estimated regression equation turned out to be ŷ = 139.2 − 6.7x. Show the 95% prediction interval estimate of the turnover rate for a particular company with an average hourly wage of $15. 81. Partial regression results from a sample of 12 observations are shown below. Fill in the missing values indicated by ( )*. Can we use the sample results shown here to reject a β = 0 null hypothesis at the 5% significance level? Explain 83. For each of the following cases, report whether the coefficient for the variable x is significantly different from 0 at the 5% significance level and explain the implications of your decision. 1. n = 13 2. n = 19 3. n = 25 ECON 3100 PROBLEM SET 4 Textbook questions: Chapter 11: 34, 37, 40, 44, 51, 57, 81, 83 Statistical investigation: Your Econ 3100 classmate Kim would like to buy a used Volkswagon Eurovan for an extended road trip this summer. Her neighbor Tim has offered to sell her his Eurovan. Tim’s Eurovan is has 75,000 miles on it. Kim and Tim agree that the van is in average condition. Tim has asked her to come up with a fair price. Your classmate has never heard of “blue book value” and sets out to estimate the value using her newly acquired knowledge of regression analysis. She checks the Seattle Times and finds a long list of Eurovans for sale. She selects a random sample of 10 vans, ranging in mileage from 59,000 to 129,000 miles. For each Eurovan, she enters the mileage (in 1000s) and the offered sales price (in $1000s) into JMP. She runs a regression predicting asking price in thousands based on mileage in thousands. She determines the relationship between mileage and asking price and also runs some estimates for the price of a Eurovan with 75,000 miles on it. The data for this example is found in the DATA folder on Canvas, entitled Eurovan.jmp. 1. What is the estimated regression equation? 2. To what extent is variation in the prices of the vans explained by differences in their mileage? 3. Give a 95% confidence interval for the coefficient on mileage. 4. Interpret the confidence interval calculated in question 3. Exactly what does it tell you? 5. Sketch a graph illustrating the estimated relationship between mileage and a van’s price. 6. Give a point estimate of the predicted price for a Eurovan in average condition with 75,000 miles on it. 7. Give a 95% confidence interval for the average price of Eurovans with 75,000 miles on them. 8. Give a 95% confidence interval (prediction interval) for the price of an individual Eurovan with 75,000 miles on it. 1 9. Explain carefully why the confidence interval you gave for the individual van is wider that that you gave for the average van. 10. Assuming that your classmate and Tim agree that his van is in average condition, what price should she offer him? What is the price you would consider fair? Explain. 11. The sample contains a Eurovan with 81,718 thousand miles on it. Assuming that the price given accurately reflects the condition of the car, do you think this van is likely to be in belowaverage, average, or above average condition, given its mileage? Explain your answer. 12. Does the residual plot give any suggestion that one of the assumptions of the regression model may be violated? If not, why not? If so, which of the assumptions may be violated, and what in the residual plot indicates this. 13. Conduct a t-test at a 0.05 significance level as to whether mileage has a statistically significant relationship to the price of a van. Be sure to provide the hypotheses, test statistics, pvalue and conclusion. Summarize the test result in a non-technical sentence. 14. Now suppose a researcher wanted to provide evidence using a 0.05 significance level, that the price of a van declines by more than $250 for each additional 1,000 on the odometer. What would be the appropriate hypotheses? The test statistic? The p-value? The conclusion? 2 Everyday statistics Please read the article “Scientific Method: Statistical Errors.” You can find it online at: http://www.nature.com/news/scientific-method-statistical-errors-1.14700 1. What is the definition of “p-value” given in the article? 2. According to the article, how did the p-value come into widespread use in scientific research? 3. The article mentions a study of online dating. What were the statistically significant findings of that study? 4. Again, referring to the study of online dating mentioned in the article, to what extent were the findings reported substantially significant? That is, how large were the differences described between couples who met online and couples who did not? 5. The article describes a phenomenon called “p-hacking,” whereby researchers manipulate their studies in order to reduce the p-values and produce statistically significant findings. List some of the ways that researchers might manipulate their results in order to produce statistically significant findings (low p-values). 6. What are some ways that researchers might go about improving their research, that is, what might they do beyond just using p-values to establish the validity of their findings? 3 G te S st MJI 0M JM 09 M J SS O. 7 TH 4D X OP 0 O'R C D'R CH SD SDSDSA MOD OD f = CO Secure https://desktop.seattleu.edu/portal/webclient/index.html#/desktop eurovan - JMP Pro File Edit Tables Rows Cols Analyze Graph Tools View Window Help o -6X eurovan D Age Mileage (1000s) 64 Price Type (full (1000) camper/MV) 30 FC 1 9 9 28 MV 2 3 4 82.345 59 27 FC 12 8 76.767 5 Year 2000 2000 1997 2001 2001 2002 1995 2000 2001 2000 8 6 7 14 7 8 9 69.218 88.275 108.077 110.608 81.718 129.591 24.9 MV 21.992 MV 19.988 MV 15 FC 13.995 MV 10.999 MV 8.888 MV 9 8 10 9 Columns (570) Year Age Mileage (1000s) Price (1000s) IL Type (full camper/MV) Rows All rows Selected Excluded Hidden Labelled 10 0 0 0 0 Start X W A 3:14 AM 2/4/2018 11 C jmptrial__1321_wi...exe 46.6/794 MB, Paused eurovan (1).jmp Show all eurovan.jmp staat3.jpg staaat2.jpg х Type here to search Q е 1 5 B wiÝ web A la 4) 3:14 AM 2/4/2018