Part IV: Regression Anahsis Problems (10 points in tota) SHOW ALL OF YOUR WORK T
ID: 3362200 • Letter: P
Question
Part IV: Regression Anahsis Problems (10 points in tota) SHOW ALL OF YOUR WORK The Excel file Salary Data provides various data of 35 employees from a company. A simple regression predicting Current salary (Y, in S) as a function of Age CX1, in years) was developed as shown below SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error 0.976 0.953 0.950 2941.90 35 ANOVA MS F Signlicance df 25591651177 2.8E 09 323.0353 6.05341E-22 32 34 276955521.7 8654860 Residual Total Standard Eror 1824.58 fStat 0.49 24.78 P-value 0.63 0.00 Lower 95% -2822.95 958.31 per 95% 4610.13 129.99 fficients 893.59 044.15 Intercent Age a. (2 pts) State the estimated regression equation based on the Excel output and predict the salary for an employee of 35 years old b. (2 pts) Is the estimated regression equation significant at the 0.05 significance level? Explain. no loecause the p-va men th signi fi canee level c. (2 pts) Find and interpret the coefficient of correlation. 893.59 is the d. (2 pts) Interpret the slope of the regression line (i.e., the coefficient associated with Age). (2 pts) Find and interpret the 95% confidence interval for the coefficient associate with Age e.Explanation / Answer
a) estimated regression equation:Y =893.59 +1044.15 X
therefore at x=35 ; estimated salary =893.59+1044.15*35=37438.84
b) as p value for above test is less then significance leve ; tehrefore regression equation is significant (Note:always when p value is less then level of significance ; test is signiificant)
c) here intercept =893.59 ; which indicate that when a person is 0 years ; salary is 893.59 which is practilcally insignificant cause a child can not have salary at age 0
d) here slope is 1044.15 ; whcih indicate that for each 1 year increase in age ; average salary increase by 1044.15
e) 95% conifdence interval from above output =958.31 to 1129.99
this interval gives 95% confidence to contain true average rate of change in salary with 1 year change