A Survey Conducted by a Research Team Was to Investigate

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The Answer is a. Using the following Excel output, we conclude that there is an overall regression relationship at the 0.05 level of significance.
$a. Using the following Excel output, we conclude that there is an overall regression relationship at the 0.05 level of significance. The p-value associated with the estimated regression parameter b₁ is 0.0013. Because this p-value is less than the 0.05 level of significance, we reject the hypothesis that β₁ = 0. We conclude that there is a relationship between the annual income and the education level at the 0.05 level of significance. Our best estimate is that if we hold the length of tenure in current employment and the age constant, a one year increase in the education level corresponds to an increase of $10,011.92 in annual income. The p-value associated with the estimated regression parameter b₂ is 0.3246. Because this p-value is greater than the 0.05 level of significance, we do not reject the hypothesis that β₂ = 0. We cannot conclude that there is a relationship between the length of tenure in current employment and the annual income at the 0.05 level of significance when controlling for education level and age. The p-value associated with the estimated regression parameter b₃ is 0.0149. Because this p-value is less than the 0.05 level of significance, we reject the hypothesis that β₃ = 0. We conclude that there is a relationship between the age and the annual income at the 0.05 level of significance. Our best estimate is that if we hold the education level and length of tenure in current employment constant, an increase in age by a year corresponds to an increase of $2,689.24 in annual income. b. The following Excel output is obtained by removing the independent variable, length of tenure in current employment (x₂), which is not significant at 0.05 significance level. Hence, this output provides the estimated multiple linear regression equation with education (x₁), age (x₃) as the independent variables. The estimated multiple linear regression equation is \hat{y}=-138671.68+9588.89 x_{1}+2234.56 x_{3} . .$
The p-value associated with the estimated regression parameter b₁ is 0.0013. Because this p-value is less than the 0.05 level of significance, we reject the hypothesis that β₁ = 0. We conclude that there is a relationship between the annual income and the education level at the 0.05 level of significance. Our best estimate is that if we hold the length of tenure in current employment and the age constant, a one year increase in the education level corresponds to an increase of $10,011.92 in annual income.
The p-value associated with the estimated regression parameter b₂ is 0.3246. Because this p-value is greater than the 0.05 level of significance, we do not reject the hypothesis that β₂ = 0. We cannot conclude that there is a relationship between the length of tenure in current employment and the annual income at the 0.05 level of significance when controlling for education level and age.
The p-value associated with the estimated regression parameter b₃ is 0.0149. Because this p-value is less than the 0.05 level of significance, we reject the hypothesis that β₃ = 0. We conclude that there is a relationship between the age and the annual income at the 0.05 level of significance. Our best estimate is that if we hold the education level and length of tenure in current employment constant, an increase in age by a year corresponds to an increase of $2,689.24 in annual income.
b. The following Excel output is obtained by removing the independent variable, length of tenure in current employment (x₂), which is not significant at 0.05 significance level. Hence, this output provides the estimated multiple linear regression equation with education (x₁), age (x₃) as the independent variables.
$a. Using the following Excel output, we conclude that there is an overall regression relationship at the 0.05 level of significance. The p-value associated with the estimated regression parameter b₁ is 0.0013. Because this p-value is less than the 0.05 level of significance, we reject the hypothesis that β₁ = 0. We conclude that there is a relationship between the annual income and the education level at the 0.05 level of significance. Our best estimate is that if we hold the length of tenure in current employment and the age constant, a one year increase in the education level corresponds to an increase of $10,011.92 in annual income. The p-value associated with the estimated regression parameter b₂ is 0.3246. Because this p-value is greater than the 0.05 level of significance, we do not reject the hypothesis that β₂ = 0. We cannot conclude that there is a relationship between the length of tenure in current employment and the annual income at the 0.05 level of significance when controlling for education level and age. The p-value associated with the estimated regression parameter b₃ is 0.0149. Because this p-value is less than the 0.05 level of significance, we reject the hypothesis that β₃ = 0. We conclude that there is a relationship between the age and the annual income at the 0.05 level of significance. Our best estimate is that if we hold the education level and length of tenure in current employment constant, an increase in age by a year corresponds to an increase of $2,689.24 in annual income. b. The following Excel output is obtained by removing the independent variable, length of tenure in current employment (x₂), which is not significant at 0.05 significance level. Hence, this output provides the estimated multiple linear regression equation with education (x₁), age (x₃) as the independent variables. The estimated multiple linear regression equation is \hat{y}=-138671.68+9588.89 x_{1}+2234.56 x_{3} . .$ The estimated multiple linear regression equation is

\hat{y}=-138671.68+9588.89 x_{1}+2234.56 x_{3}

. .

A Survey Conducted by a Research Team Was to Investigate

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