**Research Question:**Are maternal expectations and at-home school involvement strategies related to a student's expectation that he or she will attend college?

In the previous lesson, I tested the relationship between mom talked grades, a specific maternal at-home involvement strategy, and student college expectations using linear regression analysis and found a significant relationship (p=<.0001). However, r-squared, representing the percent of the variability in y explained by x, was very low at .00945. Now, I want to add more variables to my model to better explain the variability in y.

I want to test the effect of 2 other at-home involvement strategies, mom talked school other (H1WP17I) and mom helped with a school project (H1WP17J), both categorial variables with 2 levels that already include a 0 value. I also want to test the effect of mother's college expectations, considered a quantitative variable. Because this variable does not include a 0 value, I centered the data (H1WP11_c).

Here is output:

I found that after controlling for the influence of the variables, student college expectations are significantly, positively related to mom talked school other (p=0.03, beta=0.9), mom worked on school project (p=.0001, beta=.16) and mom's college expectations (p=<.0001, beta=0.3). However, my original variable, mom talked grades, no longer shows a significant relationship to student college expectations (p=0.63).

I needed to check if any of the added variables is a confounder of the association between mom talked grades and student college expectations. I added each variable to my PRAC GLM step, one by one. Each time, I found that mom talked grades had a significant p-value. Again, when I added both mom talked school other and mom worked project, and both mom worked project and mom's college expectations to the model, the p-value for mom talked grades was still significant. However, when I added mom's college expectations and mom talked school other, mom talked grades (p=.48) was not significant. Therefore, when controlling for the effects of both mom's college expectations and mom talked school other, mom talked grades does not have a significant relationship with student college expectations.

*Confounders*I needed to check if any of the added variables is a confounder of the association between mom talked grades and student college expectations. I added each variable to my PRAC GLM step, one by one. Each time, I found that mom talked grades had a significant p-value. Again, when I added both mom talked school other and mom worked project, and both mom worked project and mom's college expectations to the model, the p-value for mom talked grades was still significant. However, when I added mom's college expectations and mom talked school other, mom talked grades (p=.48) was not significant. Therefore, when controlling for the effects of both mom's college expectations and mom talked school other, mom talked grades does not have a significant relationship with student college expectations.

*Multiple Regression Analysis*

I want to learn more about the relationship between student college expectations and maternal college expectations. First, I used the GLM procedure to test the linear relationship between the two. The significant p-value and positive parameter estimate shows that maternal college expectations are positively associated with student college expectations.

Next, I tried a quadratic model. The p-value for H1WP11 squared was negative, suggesting that the fit line starts low, curve upwards and then curves down again. The r-squared value also increase from about 12% to about 13% .

Next, I want to evaluate the fit of this model.

*Standardized Residuals*: The graph of the standardized residuals showed that a large portion of the results were more than 2 standard deviations from the mean, suggesting that this is not a very good fit. In the future, I will have to add more variables to my model to better explain the variability in y.