Best Subsets Regression: y versus x1, x2, x3 Response is y R-Sq Vars R-Sq (adj) PRESS 1 99.1 99.0 341.1 78.0 76.8 8523.2 99.2 99.1 325.6 99.1 99.0 388.1 1 22 2 2 R-Sq (pred) 98.9 72.3 98.9 98.7 Mallows Cp 7.1 542.9 5.7 9.0 X S 1 3.9403 19.389 X 3.7418 X 4.0433 XmX X X 2 3 X X X X
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24. Using the adjusted R2, which variables is/are included in the best set of the model?
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- Special Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Gray Wolves in WisconsinGray wolves were among the first mammals protected under the Endangered Species Act in the 1970s. Wolves recolonized in Wisconsin beginning in 1980.Their population grew reliably after 1985 as follows: Year Wolves Year Wolves 1985 15 1993 40 1986 16 1994 57 1987 18 1995 83 1988 28 1996 99 1989 31 1997 145 1990 34 1998 178 1991 40 1999 197 1992 45 2000 266 a. Explain why an exponential model may be appropriate. b. Are these data exactly exponential? Explain. c. Find an exponential model for these data. d. Plot the data and the exponential model. e. Comment on your graph in part d. Which data points are below or above the number predicted by the exponential model?XYZ Corporation Stock Prices The following table shows the average stock price, in dollars, of XYZ Corporation in the given month. Month Stock price January 2011 43.71 February 2011 44.22 March 2011 44.44 April 2011 45.17 May 2011 45.97 a. Find the equation of the regression line. Round the regression coefficients to three decimal places. b. Plot the data points and the regression line. c. Explain in practical terms the meaning of the slope of the regression line. d. Based on the trend of the regression line, what do you predict the stock price to be in January 2012? January 2013?Special Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Postal RatesThe table below shows the cost s, in cents, of a domestic first-class postage stamp in the United States tyears after 1900. t=time,inyearssince1900 s=costofstamp 19 2 32 3 58 4 71 8 78 15 85 22 95 32 102 37 109 44 116 47 a.Use exponential regression to model s as an exponential function of t. b.What cost does your model give for a 1988 stamp? Report your answer to the nearest cent. The actual cost was 25cents. c.Plot the data and the exponential model.
- Special Rounding Instructions. For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Caloric Content Versus Shell Length In 1965, Robert T.Paine gathered data on the length L, in millimeters, of the shell and the caloric content C, in calories, for a certain mollusk. The table below is adapted from those data. L=length C=Calories 7.5 92 13 210 20 625 24 1035 31 1480 a.Find an exponential model of calories as a function of length. b.Plot the graph of the data and the exponential model. Which of the data points show a good deal less caloric content than the model would predict for the given length? c.If length is increased by 1millimeter, how is caloric content affected?Use Excel to find an estimated linear regression equation using X1 and X2 as the independent variables and Y as the dependent. Put your output on a fresh sheet. Then answer the following questions (excel chart in the picture) Write down the estimates regression equation What is the expected value of Y if X1 is 240 and X2 is 290? Show your calculation at a 5%level of significance, are the true coefficients of X1 and X2 different from zero? Justify briefly using numbers from your excel output. 4. Using Excel, determine a 97% confidence interval for the true coefficient of X1a) Give the estimated regression function. Also, give the hypothesis, test statistic and the rejection region to assess whether the interactive terms contribute to reducing the mean variation of the response variable. Test at ? = 0.05. Then How can the conclusion be confirmed? Explain the result.
- 27. Using the stepwise regression, what is the value of adjusted R2 of the last step?Using the regression line attached. The plot: a) reveals sure evidence that the population slope is unequal to 0 b) reveals sure evidence that the sample slope is unequal to 0 c) can be used alone to reject the null hypothesis that the population slope is unequal to 0 d) can be used alone to reject the null hypothesis that the population slope is equal to 0 e) a and c f) a and dWhich statistic is associated only with multiple regression and not with simple regression? adjusted R2 partial F test estimated or predicted value z-test
- Disk drives last time Here is a scatterplot of the residu-als from the regression of the hard drive prices on their sizes from Exercise 18.a) Are any assumptions or conditions violated? If so,which ones?b) What would you recommend about this regression?magine that you first estimate an OLS regression with a random sample of 100 observations and then re-estimate the same regression with 100 additional observations which are also randomly sampled. What would you expect to happen as the sample size increases? a. R-squared increases b. t-statistic decreases c. Sum of squared residuals decreases d. the standard error gets smallerThis assignment involves putting together a scenario where you are asking a question that requires analyzing data - doing a hypothesis test or determining what variables are statistically significant using your favorite statistical analytical tool learned in this course. The tools you have learned include z and t-test one population, two population, and ANOVA (regression analysis and prediction using linear regression or multivariable regression). Pretend you are the CEO and the analyst doing the analysis. Write the scenario using APA style formatted paper: Title page, Introduction, Body (with category sectional headings), Conclusion, and Reference.