Question

The production of wine is a​ multi-billion-dollar worldwide industry. In an attempt to develop a model of wine quality as judged by wine​ experts, data was collected from red wine variants from a particular type of foreign wine. A multiple linear regression model was developed from a sample of 45 wines. The model was used to predict wine​ quality, measured on a scale from 0​ (very bad) to 10​ (excellent) based on the alcohol content​ (%) and the amount of chlorides. Use the accompanying results to complete parts​ (a) and​ (b) below.

Variable Intercept Alcohol, Xy Chlorides, X2 Coefficient 1.02983 0.45032 -9.01536 Standard Error 1.35423 0.10325 3.67931 t Statistic 0.76 4.36 p-value 0.2256 0.0001 - 2.45 0.0185 a. Construct a 95% confidence interval estimate of the population slope between wine quality and the percentage of alcohol. OsBs (Round to four decimal places as needed.)

b. At the 0.05 level of​ significance, determine whether each independent variable makes a significant contribution to the regression model. On the basis of these​ results, indicate the independent variables to include in this model. Choose the correct hypotheses for X1 below.

Choose the correct hypotheses fo X2 below.

Answer 1

CI = , $t 2,0.05 SE (5) = 0.45032+(2.018) (0.10325) = 0.4503+0.2084 = (0.4503 – 0.2084.0.4503+0.2084) =(0.2419,0.6587) The 95% confidence interval is 0.2419 SB 50.6587. (b) HA=0 H:A#0 star = 4.36 p-value = 0.0001

Reject Ho. There is sufficient evidence that X, makes a signficant contribution to the regression model. H: B=0 "H:80 tsu =-2.45 p-value = 0.0185 Reject Ho. There is sufficient evidence that X, makes a signficant contribution to the regression model A. Include both variables X and X -