answer all questrions and SHOW ALL work 1)Use the following dataset to calculate
ID: 3129750 • Letter: A
Question
answer all questrions and SHOW ALL work
1)Use the following dataset to calculate the answers by hand. Round all values to 4 decimals.
The following table gives information on salaries in thousands of dollars, years of education past high school, and years of experience of the firm. These observations were randomly drawn from a large firm.
a)Write the hypothesized regression equation.
b)Calculate the estimates for the intercept and slopes.
c)Calculate the estimate of the regression standard error.
d)Calculate and interpret R2.
e)Calculate and interpret adj-R2.
f)Calculate and interpret the simple correlation coefficient.
Annual Sallary Year of school past high school years experience with film 30 4 10 20 3 8 36 6 11 24 4 9 40 8 12Explanation / Answer
First transform the problem in linear regression setup.Annual salary is taken as 'Y' the dependent variable and Year of school past high school,years experience with film are taken as the regressors X1, X2.
First input these data in the minitab statistical software:-
Y X1 X2
30 4 10
20 3 8
36 6 11
24 4 9
40 8 12
Regression Analysis: Y versus X1, X2
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 2 270.500 135.250 180.33 0.006
X1 1 0.100 0.100 0.13 0.750
X2 1 30.250 30.250 40.33 0.024
Error 2 1.500 0.750
Total 4 272.000
Model Summary
S R-sq R-sq(adj) R-sq(pred)
0.866025 99.45% 98.90% 96.57%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant -23.75 5.53 -4.29 0.050
X1 -0.250 0.685 -0.37 0.750 10.00
X2 5.500 0.866 6.35 0.024 10.00
Regression Equation
Y = -23.75 - 0.250 X1 + 5.500 X2
a) the regression equation is: Y = -23.75 - 0.250 X1 + 5.500 X2
b)the estimates for the intercept is -23.75 and
for slopes are -0.25 and 5.5
c) SS(regression)=2705
SS(error)=150
d) R^2=0.9945
Interpretation:It indicates how well data fit a statistical model.R^2 is a statistical measure of how close the data are to the fitted regression line. R^2 = Explained variation / Total variation.
Here R^2=09945 indicates that the model explains all the variability of the response data perfectly.
e) adj R^2=0.989
Interpretation: The adjusted R^2 tells you the percentage of variation explained by only the independent variables that actually affect the dependent variable.
Here Adjusted R square=0.989 calculates the proportion of the variation in the dependent variable accounted by the explanatory variables.
f) In linear least squares regression with an estimated intercept term, R^2 equals the square of the correlation coefficient between the observed and modeled data values of the dependent variable.
simple correlation coefficient=sqrt(0.9945)=0.9972462
Interpretation: There exixst high positive linear relationship between annual salary with Year of school past high school and years experience with firm.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.