The regression model that is to be estimated is
where is a random disturbance
the estimated regression equation is
a) Using this
We know
k=4 is the number of independent variables
Sum of square Error (residuals), SSE = 22,387,821
degrees of freedom residuals = n-k-1 = 88
Sum of square Total (residuals), SST = 46,151,118
degrees of freedom total is n-1 = 92
The adjusted R-square is
ans: The adjusted R-square is 0.4929
b) We want to test the following hypotheses
The test statistics has F distribution. The test statistics is given below
The test statistics is F=23.35 with numerator df=4 and denominator df=88
Using F table for alpha=0.05 and numerator df=4 and denominator df=120 (The closest we can get to 88) we get the critical value of F = 2.45
We will reject the null hypothesis if the test statistics is greater than the critical value.
Here the test statistics is 23.35 and it is greater than the critical value, 2.45. Hence we reject the null hypothesis.
We conclude that the overall model is significant
c) There would be positive linear relationship between salary and experience if the slope coefficient of Experience in the regression model is greater than 0.
That is we want to test the following hypotheses
This is a right tailed test (the alternative hypothesis has ">").
The hypothesized value of (from the null hypothesis) is
Using the following
the test statistics is
The degrees of freedom for t statistics is n-k-1=88
The p-value given in the output is 0.034 is for a 2 tailed test. For one tailed test the p-value is half of that, that is p-value=0.034/2=0.017
We will reject the null hypothesis if the p-value is less than level of significance
Here the p-value is 0.017 and it is less than 0.05 level of significance. Hence we reject the null hypothesis.
We conclude that there is a positive linear relationship between Salary and Experience, after accounting for the effect of the variables, Sex, Education, and Months
d) the predicted salary for Sex=1 (man), Education = 15, Experience = 20 , months=10 is
ans: The salary for a man with 15 years of education, 20 months of experience and 10 months with in the company is $5,852.4
(Important: In the question pasted, the unit of the salary is not given. Please express the figure 5,852.4 accordingly)
e) To know if there is an interaction between Sex and Experience we will modify the model as below
If the interaction is significant it means that the coefficient
The salary model for a man is (by setting Sex=1)
The salary model for a woman (by setting sex=0) is
It means that the predicted salary changes by for one month increase in the experience for a man compared to for a woman (while keeping other variables the same)
3. The table below shows the regression output of a multiple regression model relating the beginn...
*ANSWERS IN BOX ARE INCORRECT* Consider the following ANOVA table for a multiple regression model. Complete parts a through e below. Source Regression 3 3,600 1200 20 Residual 35 2,100 60 Total df SSMSF 38 5,700 a. What is the size of this sample? n41 b. How many independent variables are in this model? c. Calculate the multiple coefficient of determination. R0.5882 Round to four decimal places as needed.) d. Test the significance of the overall regression model using α=0.05...
Table 2 below shows cross-sectional regression results from the study of Beck, Degryse, and Kneer (2014).1 The dependent variable is the economic growth (GDP per capita growth) of different countries averaged over the period 1980- 2007. The explanatory variables are defined as follows: intermediation is a proxy for the size of financial sector and equal to the logarithm of the credit over GDP for every country in the sample; initial GDP is the logarithm of the GDP per capita in...