Problem The following data is the salary Y of a person versus the number of year

Question

Problem The following data is the salary Y of a person versus the number of years with the company and their degree attained, where 1-bachelor's degree 2:Master's Degree 3 Doctorate Degree Attained Salary Y Years with company x1 x2 32000 37400 39000 42000 45000 49000 51000 55000 59000 10 12 15 Find the multiple regression line that estimates salary based on years with the company and degree attained What factor is more important to salary, years with the company or degree attained? How much would I expect salary to increase for each higher degree attained?

Explanation / Answer

Here given that dependent variable is salary and there are two independent variables as years with the company and degree attained.

Since this is the problem of multiple regression.

We can do multiple regression in MINITAB.

steps :

ENTER data into MINITAB sheet --> STAT --> Regression --> Regression --> Response : y --> Predictors : x1 and x2 --> Results : select second option --> ok --> ok

Output :

Welcome to Minitab, press F1 for help.

Regression Analysis: y versus x1, x2

The regression equation is
y = 26825 + 1823 x1 + 1838 x2

Predictor Coef SE Coef T P
Constant 26825 1279 20.97 0.000
x1 1822.9 313.5 5.81 0.001
x2 1838 1434 1.28 0.247

S = 1450 R-Sq = 98.0% R-Sq(adj) = 97.3%

Analysis of Variance

Source DF SS MS F P
Regression 2 604997841 302498921 143.92 0.000
Residual Error 6 12611048 2101841
Total 8 617608889

Here we can test two hypothesis :

1) Here we have to test the hypothesis that,

H0 : Bj=0 Vs H1 : Bj not= 0

where Bj is population slope for jth independent variable.

Assume alpha = level of significance = 5%= 0.05

Test statistic follows F-distribution.

F = 143.92

P-value = 0.000

P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : Atleast one of the slope is differ than 0.

We get significant result about F-test.

Now we have to test which slope significantly differs.

For this we have to test the hypothesis that,

H0 : B = 0 Vs H1 : B not= 0

where B is population slope for independent variable.

Assume alpha= 0.05

Here test statistic follows t-distribution.

P-value for x1 (years with company) is 0.001 < alpha.

Reject H0 at 5% level of significance.

Conclude that population slope for Years with company is differ than 0.

We get significant result about years with company so we include this variable in the model.

P-value for x2 (degree attained) is 0.247 alpha.

Accept H0 at 5% level of significance.

Conclude that population slope for Years with company is 0.

We get insignificant result about degree attained so we exclude this variable from the model.

R-sq = 98.0%

It expresses the proportion of variation in dependent variable which is expressed by variation in independent variables.

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