TR 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 SALES 88 80 96 76 80 73 58 116 104 99 64 126 94 71 111 109 100 TV 100 99 101 93 95 95 80 116 106 105 90 113 96 98 109 102 100 RADIO 95 99 103 95 102 94 89 112 110 87 90 101 100 85 99 101 93 NEWS 87 98 101 91 88 84 74 102 105 97 88 108 89 78 109 108 102 2 3 4 1 2 3 4 1 127 99 82 67 100 78 115 83 107 108 95 91 114 93 115 97 108 100 69 95 91 80 85 105 110 95 90 85 103 80 104 83 year Month 1999 Jan Crates 20400 Feb 13600 Mar 17000 Apr 30600 May 23800 Jun 17000 Jul 27200 Aug 30600 Sep 34000 Oct 45900 Nov 40800 Dec 2000 Jan 30600 13600 Feb 23800 Mar 30600 Apr 25500 May 27200 Jun 30600 Jul 23800 Aug 47600 Sep 37400 Oct 45900 Nov 44200 Dec 2001 Jan 17000 20400 Feb 13600 Mar 30600 Apr 22100 May 23800 Jun 30600 Jul 28900 Aug 34000 Sep 42500 Oct 47600 Nov 30600 Dec 30600 2002 Jan 25500 Feb 20400 Mar 23800 Apr 30600 May 25500 Jun 30600 Jul 34000 Aug 37400 Sep 44200 Oct 47600 Nov 34000 Dec 2003 Jan 37400 25500 Feb 37400 Mar 30600 Apr 30600 May 27200 Jun 34000 Jul 47600 Aug 47600 Sep 34000 Oct 51000 Nov 37400 Dec 47600 1) A real estate agent wants to make a regression equation to help her predict the price of houses in a specific neighborhood. She uses the number of bedrooms, the square footage and the age of the houses in her initial collection. Using the graphs and outputs, answer the following questions: a) What are the independent and dependent variables? b) Discuss the feasible linearity by using the scatterplots below. The output is on the next page - please use it to answer the rest of the questions. Predictor Constant sq footage age numb rooms Coef -0.52 0.05646 -0.3804 6.842 S = 21.4788 SE Coef 32.91 0.01382 0.3739 3.148 R-Sq = 71.2% T -0.02 4.09 -1.02 2.17 P 0.987 0.001 0.322 0.043 R-Sq(adj) = 66.6% Analysis of Variance Source Regression Residual Error Total DF 3 19 22 SS 21640.9 8765.4 30406.3 MS 7213.6 461.3 F 15.64 P 0.000 c) Discuss the coefficient of determination and the correlation. Use the proper ones for multiple regression and answer in sentences. Aka R^2adj and Radj. d) Run the F test and tell us if further analysis gives any information. (Set up Ho and Ha and discuss). e) If you rejected the null from the F test, then looking at the output, what variables do you think are important to the model? (Give this a try - we will discuss it in class) f) Predict the price of a house that is 30 years old, 10 rooms and 2500 square feet. 2) Open the excel file (homework_for_MLR) Choose the sales_by_adv file (along the bottom tabs) Run a multiple linear regression using sales as the dependent variable where quarter is the dummy variable and TV, Radio, and News are the advertising media (make sure to re format the data properly first). Then answer the following questions: a) Discuss the R^2adj and Radj (to see if this is a feasibly good model) b) Write out the equation of the model and define all the coefficients. c) Run an F test. d) Are any slopes problematic? Which ones? Give some reasons why you think this has occured? e) Predict the next year of sales if the following are the advertising budgets: QTR 1 2 3 4 TV 105 98 102 95 RADIO 90 93 103 92 NEWS 87 92 101 91 1) Open the excel file (homework_for_MLR) Choose the crate file (along the bottom tabs) Run a multiple linear regression (with trend) using crates as the dependent variable where months are the dummy variable (make sure to re format the data properly first). Then answer the following questions: f) Discuss the R^2adj and Radj (to see if this is a feasibly good model) g) Write out the equation of the model and define all the coefficients. h) Run an F test. i) Are any slopes problematic? Which ones? Give some reasons why you think this has occured? j) Predict the next year of crates needed