Question

The accompanying set of dependent and independent variables to complete parts a through c below.

Click the icon to view the data set.
Using technology, construct a multiple regression model with the given data.
(9.571)+ (0.853)x₁+ (0.244x₂
ound to three decimal places as needed.)
Set of dependent and independent variables
y 10 12 16 16 21 24 28 33
x1 1 5 5 9 7 10 17 20
x2 16 11 14 11 1 8 6 3

Answer 1

The multiple regression model is attached below.

The R-squared value is 0.928, which indicates that the model explains 92.8% of the variability in the dependent variable. The adjusted R-squared value is 0.899, which is also a good value.

The F-statistic is 32.30 and the p-value is 0.00138, which means that the model is statistically significant.

The coefficients of x1 and x2 are both positive, which means that both x1 and x2 have a positive relationship with the dependent variable.

The coefficient of x2 is negative, which means that x2 has a negative relationship with the dependent variable.

The standard errors of the coefficients are relatively small, which means that the estimates are precise.

The t-statistics of the coefficients are all greater than 2 in absolute value, which means that the coefficients are statistically significant.

Overall, the multiple regression model is a good fit for the data.