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COMM 291
Jonathan Berkowitz

Question 1 a) The scatterplot shows a positive, moderately strong, linear relationship between price and size. Price versus Size 300 y = 0.0766x + 21.398 250 200 150 Price ($1000) 50 0 0 500 1000 1500 2000 2500 Size (Sq. Ft) b) Please see above for regression line. The estimated regression equation for predicting price from size is: ̂ c) Ho: Ha: √ P-value = TDIST(4.601, 28) < 0.001 This small P-value indicates that there is a significant linear relationship between Size and Price . d) The 95% CI for the slope is = TINV(0.05, 28) = 2.048. e) ̂ The predicted selling price is $143,941, so it is not advisable for the client to buy the house; the asking price of $180,000 for the house is unreasonably high. f) The 95% CI for the mean is = TINV(0.1, 28)  1.701. √ g) The 95% PI is = √ Question 2 a) H 0 All 13 explanatory variables have a coefficient of zero. H : At least one of the variables has a non-zero coefficient. a The degrees of freedom are df1 = k = 13 and df2 = n – k – 1 = 2215. P-value = FDIST(F, df1, df2) = FDIST(71.34,13,2215) = 0. Therefore, we conclude that at least one of the coefficients is not zero. b) This tells us that 29.7% of the variation in interest rates is explained by the 13 variables. c) H 0  i 0 and Ha:  i 0. The degrees of freedom are 2215. Therefore, values that are less than -1.96 or greater than 1.96 will lead to rejecting the null hypothesis. = TINV(0.05, 2215) = 1.96. d) The variables that are significantly different from zero are the following:: loan size, length of loan, percent down payment, co-signer, unsecured loan, total income, bad credit report, young borrower, own home and years at current address. If a t-stat is concluded to be not significant, that means the corresponding variable does not contribute significantly to the prediction of the response variable when the other variables are in the model. e) The interest rate is lower for larger loans, lower for longer length loans, lower for a higher percent down payment, lower when there is a co-signer, higher for an unsecured loan, lower when there is higher total income, higher when there is a bad credit report, higher when there is a young borrower, lower when the borrower owns a home and lower when the years at current address is higher. f) There are two ways of constructing a more parsimonious model: 1. Remove the predictor variables that are not significant from the full model, one at a time, based on the individual t-tests (P-values) until all
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