Asked by Andrew Oriold on Jun 04, 2024
Verified
The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female) .
= 30 + .7x1 + 3x2
Also provided are SST = 1200 and SSE = 384.At the 5% level, the model
A) is significant.
B) is not significant.
C) would be significant if the sample size was larger than 30.
D) has significant individual parameters.
Estimated Regression Equation
A formula that models the relationship between one or more independent variables and a dependent variable.
Yearly Income
The total amount of money earned by an individual or entity in one calendar year from all sources before any deductions.
SSE
Sum of Squares due to Error, a measure indicating the discrepancy between the data and an estimation model.
- Calculate and interpret the significance of regression models using F-tests and t-tests.
Verified Answer
F = (SSR / k) / (SSE / (n - k - 1))
Where SSR is the regression sum of squares, k is the number of predictors in the model, SSE is the error sum of squares, and n is the sample size.
Using the given information, we can calculate that SSR = SST - SSE = 1200 - 384 = 816, k = 2, and n = 30. Substituting into the F formula, we get:
F = (816 / 2) / (384 / 27) = 11.25
To find the critical value for F at the 5% level, we look up the F distribution with 2 and 27 degrees of freedom in a table or use a calculator. The critical value is approximately 3.35.
Since our calculated F value (11.25) is greater than the critical value (3.35), we reject the null hypothesis that all the coefficients in the model are zero. Therefore, we conclude that the model is significant at the 5% level.
Learning Objectives
- Calculate and interpret the significance of regression models using F-tests and t-tests.
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