Concept explainers
a.
Construct a table of sample regression coefficients and discuss the changes in the regression coefficients as the regression equation changes to include different subsets of predictor variable.
b.
Construct a table of estimated standard deviations and discuss the changes in the standard deviation as the regression equation changes to include different subsets of predictor variable.
c.
Construct a table of t-statistics and discuss the changes in the standard deviation as the regression equation changes to include different subsets of predictor variable.
d.
Consider a table of VIF and discuss the changes in the standard deviation as the regression equation changes to include different subsets of predictor variable.
e.
Give an assessment of the severity of the multicollinearity problem in the given regression analysis.
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Introductory Statistics (10th Edition)
- Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?arrow_forwardThe following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.arrow_forwardSuppose the Sherwin-Williams Company is interested in developing a simple regression model with paint sales (Y) as the dependent variable and selling price (P) as the independent variable. Complete the following worksheet and then use it to determine the estimated regression line. Sales Region Selling Price Sales ($/Gallon) (x 1000 Gal) ii xixi yiyi xixiyiyi xi2xi2 yi2yi2 1 15 160 2,400 225 25,600 2 13.5 220 2,970 182.25 48,400 3 16.5 140 2,310 272.25 19,600 4 14.5 190 2,755 210.25 36,100 5 17 120 2,040 289 14,400 6 16 160 2,560 256 25,600 7 13 210 2,730 169 44,100 8 18 150 2,700 324 22,500 9 12 220 2,640 144 48,400 10 15.5 190 2,945 240.25 36,100 Total 151 1,760 26,050 2,312 320,800 Regression Parameters Estimations Slope (ββ) -16.49 Intercept (αα) 424.98 In words, for a dollar increase in the selling price, the expected sales will increase by 2,640 gallons in a given sales region.…arrow_forward
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- Consider the following linear regression model that relates income per capita in thousand dollars of a country i (GDP P Ci), with its percentage of the population in the agricultural sector (P Ai): Model : GDP P Ci = β0 + β1P Ai + ui (a) Explain in words how to interpret parameters β0 and β1. What sign do you think these parameters might have? Explain. (b) Draw the (population) regression line associated with this model assuming that parameters β0 and β1 have the sign you have indicated in answering question (2a). Explain the meaning of this regression line.arrow_forwardConsider the following model:? = ?? + ?,known as the Classical Linear Regression Model (CLRM), where y is the dependent variable, X is the set of independent variables, ? is the vector of parameters to be estimated and ? is the error term. Present and discuss the R2 and the adjusted R2. Discuss pros and cons of each of the two statistics.arrow_forwardAn analyst fits the following regression model using 1,000 sample data: Profit = 30.23 + 20.62 Service Quality + 5.25 Product Quality + ε The Service Quality was recorded on a 6-point Likert scale by their customers, while the Product Quality was rated at 0 – 100 marks by the engineers. The analyst finds that the p-value of the Global F test is 0.000001, and the p-values of the two individual t tests are 0.045 and 0.039 respectively. The 4 assumptions about the random error term are all satisfied. Taking 5% significance level, the analyst concludes that Product Quality is a less important factor than Service Quality in affecting the Profit, hence he recommends the company to put all resources in enhancing the Service Quality in order to maximize Profit. Do you agree with his conclusion? List three reasons to support your answerarrow_forward
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning