Regression Analysis

Summery

The primary objective of this is to predict and find the “wife's education level (wifeduc, dependent variable) based on the husband's education level (husbeduc, independent variable)." (CTU, 2022) We use a Linear Regression analysis in SPSS using a dependent variable and an independent variable. Finally, we calculate the predicted number and make the scatterplot to show the “line of best fit of "the wife's education level based on the husband.” (CTU, 2022)

Analysis and methodology

Using a Linear Regression model in SPSS, we compute the gss.sav datasets in SPSS with GSS(n.d.) with the following code, and we analyze the outcomes in the following sections.

“REGRESSION

  /MISSING PAIRWISE

  /STATISTICS COEFF OUTS CI(95) R ANOVA

  /CRITERIA=PIN(.05) POUT(.10)

  /NOORIGIN

  /DEPENDENT wifeduc

  /METHOD=ENTER husbeduc

  /SCATTERPLOT=(*ZRESID ,*ZPRED)

  /RESIDUALS DURBIN HISTOGRAM(ZRESID) NORMPROB(ZRESID)

  /CASEWISE PLOT(ZRESID) OUTLIERS(3)

  /SAVE COOK.”

Results, reports, charts, and assumptions

The results of Model Summery, ANOVA, Coefficients, and scatterplots are here based on the outcomes of the SPSS report, which is attached to the assignment submissin

 

 

 

The Scatterplot and line of the best fit to data

Based on our general Linear Regression Equation model (Y = a + bX), where b is the slope, and a is the y-intercept, we can identify the line of best fit for our data as the following scatterplot.

The Linear Regression Equation

The Coefficients Model (table below) shows that both coefficient values (.000, .000) are significant ( < 0.05 ), all requirements are met, and we can reject the hypothesis.

We can use the following calculations for the regression equation based on this model “Y = a + bX”. In the formula, X represents the (independent value) husband's years of education “X = 14”, Y is the (dependent value) wife's years of education, b is the slope, and a is the y-intercept. “Y = 6.433 + (0.505 * 14) = 6.433 + 7.07 =  13.503” is the wife's “predicted number of years of education, when the husband has 14 years of education.”

NOTE: as you can see on the above scatterplot, it rounded the equation as “Y = 6.41 + (0.51 * 14) = 13.55” years of education predicted for the wife.

Proportion of Variance

To evaluate the Proportion of Variance in our Model Summary (table below), we focus on the R (Pearson Correlation) and R Square (Proportion of Variance). It tells us how close our data are fitted to the line, and “the independent variable explains (31.4%) of the variability of the dependent variable. Moreover, the Adjusted R-Squared (31.3%) improves the model only if the improvement is greater than that from only chance.”

 

References

Dr. Todd Grande - Linear Regression in SPSS. (2014, June 11). YouTube. Retrieved 2022, from https://www.youtube.com/watch?v=U2p16pCHW3c&t=10s

CTU, (2022). Colorado Technical University. Student’s restricted panel. Retrieved 2022, from Colorado Technical University restricted area of assignments.