About Linear regression

When we want to predict the value of one variable based on the value of another, we utilize linear regression. The value we are aiming to forecast is known as the dependent variable, while the one we are predicting is known as the independent variable.

The effect of GPA on Post-MBA wages will be examined in the research hypothesis. The following are the null and alternative hypotheses:

H0: B1 = 0

H1: B1 ≠ 0

Post-MBA wages will be the dependent variable, and GPA will be the independent variable. In other words, the research topic looks into how obtaining a GPA affects post-MBA wages.

The outcomes of regression

When the linear regression was run of salaries (dependent variables) against GPA (independent variable) using IBM SPSS, the following output resulted.

Model Summary

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

Change Statistics

R Square Change

F Change

df1

df2

Sig. F Change

1

.048a

.002

-.009

1.260

.002

.205

1

87

.652

a. Predictors: (Constant), GPA

ANOVAa

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

.326

1

.326

.205

.652b

Residual

138.146

87

1.588

Total

138.472

88

a. Dependent Variable: Salaries

b. Predictors: (Constant), GPA

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

95.0% Confidence Interval for B

B

Std. Error

Beta

Lower Bound

Upper Bound

1

(Constant)

1.750

.933

1.875

.064

-.105

3.605

GPA

.118

.260

.048

.453

.652

-.399

.634

a. Dependent Variable: Salaries

Interpreting and Reporting the Output of Regression Analysis

Model Summary

The model summary table has the “R” value, which measures the quality of prediction of the dependent variable (Salaries). The value of R is 0.048 from the model summary table. The R-squared is the coefficient of determination, in other words, the proportion of variance in the dependent variable. In our case, it is 0.002, signifying that 0.2% of the variability of the dependent variable salaries is explained by the independent variable. The important value is the adjusted R-squared which -0.009.

Statistical significance

The ANOVA table shows F-ratio which test if the regression model is a good fir of the data. The F (1, 87) value is 0.205 but the p-value is 0.652. since the p-value is greater than 0.05, the regression model is not a good fir of the data.

Estimated model coefficients

We use the Coefficients table can be used to form a general equation of the relationship between Salaries and GPA. The equation is

Salaries = 1.72 + 0.118*(GPA)

Using the above analysis, we can conclude that we have rejected the null hypothesis (H0: B1 = 0) since our constant B1 = 0.118.

NB: I had to combine the SR50000999 – SR25000029999 into one variable which I have named it SR[salaries]. However, I realized that the new variable SR was exact to the variable “MonthlybasesalariesbeforetheMBA”