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	Coefficient	Standard Error	t Statistic	​p-value
Intercept	1.02983	1.35423	0.76	0.2256
​ Alcohol, X1	0.45032	0.10325	4.36	0.0001
​ Chlorides, X2	−9.01536	3.67931	−2.45	0.0185

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 X1below

O B. Ho: B1 60 H4: B1 = 0 O A. Ho: B4 = 0 H1:34 0 O C. Ho: B4 #1 H: B1 = 1 OD. Ho: B1 = 1 H: B1 1 Find the test statistic for X1. ESTAT=1 (Type an integer or decimal rounded to two decimal places as needed.) Determine the p-value for X1. p-value = (Type an integer or decimal rounded to four decimal places as needed.) Reach a conclusion for X1. ere sufficient evidence that kes a significant contribution to the regression model.

Answer 1

Ans:

Option A is correct.

HO: B1 = 0

H1:31 0

Test statistic:

t=0.45032/0.10325

t=4.36

df=45-2-1=42

p-value=tdist(4.36,42,2)=0.0001

As,p-value<0.05,so

Reject H₀.There is sufficient evidence that X₁ makes a significant contribution to the regression model.