Question 1. We have data that give the selling price at auction of 32 antique gr

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Question 1. We have data that give the selling price at auction of 32 antique grandfather clocks. Also recorded is the age of the clock and the number of people who made a bid. Here ids the description of the variables Variable Age (1)Age of the clock (years) Bidders (xa) Number of individuals participating in the bidding Price (y) Selling price (pounds sterling) Description (a). Write down a first order multiple regression model using Price as response and the Age and number of bidders as predictors. The first order model was fit to the data, leading to the following Minitab regression output. Regression Analysis: Price versus Age, Bidders, AgeBidders Predictor Constant AGE(X1) NUMBIDS(X2) 85.953 8.729 9.85 0.000 Coef SE Coef TP -1339.0 . 173.8-7.70 0.000 12.7406 0.9047 14.08 0.000 S= 133.485 R-Sq= 89.2% R-Sq(adj)=88.5% Analysis of Variance DF MS Source Regression Residual Error 29 516727 17818 Total 2 4283063 2141531 XXXX XXXX 31 4799790 (b). Using the output, write down the estimated first order multiple regression model. (c). Interpret the value of

Explanation / Answer

Question 1

The estimated regression model is formed using the coef values from the table

Price = -1339 +12.74*Age +85.9*numbids

The value of beta1 is 12.74 , this means that for every unit change in the value of age , the value of Price would change by 12.74 units

the p value of Beta1 , as seen from the output table is 0.00 , which is less than 0.05 , hence we conclude beta1 is not zero as we reject the null hypothesis in favor of alternate hypothesis

The 95% CI for bidders is

point +- 1.96*SE , where 1.96 is for 95% CI from the Z table

85.953 +- 1.96*8.729

68.84 , 103.06

The r2 value is 89.2% , this means that the model is able to explain 89.2% variation in the data

Please note that we can answer only 4 subparts of a question at a time , as per the answering guidelines

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