Question

A company manager is interested in analyzing the relationship between years of working experience and the salary of their employees. He has collected the data from 30 employees of their years of experience and the salary. Below provided is a partial regression output from R. Use the provided information to answer below questions Coefficients: (Intercept) YearsExperience Estimate Std. Error t value Pr(>ltl) 25792.2 2273.1 9450.0 --- Signif. codes: O '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1'' 1 Analysis of Variance Table Response: Salary Df Sum Sq Mean Sq F value Pr(>F) YearsExperience 1 2.0857e+10 2.0857e+10 622.51 < 2.2e-16 *** Residuals 28 9.3813e+08 3.3505e+07 --- Signif. codes: O '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 '' 1

Answer 1

SOLUTION i: Let $\beta1$ be the coefficient of YEARS OF EXPERIENCE

NULL HYPOTHESIS Ha: $\beta1=0$

ALTERNATIVE HYPOTHESIS Ha: $\beta1\ne0$

ii) Under null hypothesis test statistic is

Test statistic t= coefficient of b1/s.e(b1)

Since standard error of b1 is not given we will make use of TABLE 2

From table 2 we have

F=622.51

As we know that

F= t^2

622.51= t^2

t= sqrt(622.51)

t= 24.95

Degrees of freedom= 30-2=28

P value= 0.0000 (By using Excel's function TDIST)

iii) Since P value is SMALLER than the level of significance therefore SIGNIFICANT.

Decision: REJECT H0.

Conclusion: We have sufficient evidence to show that more years of working experience lead to higher salaries at 0.05 level of significance.