Linear Regression, Essay Example

Independent T-Test Samples

One-Way Anova

General Linear Regression

The t-test is simply comparing the language score means between males and females based on the correlational coefficient. In this example, the female mean score (52.990) is higher than the male mean score (46.98), when the size of the sample is taken into account, a t-score of 3.01 is calculated (p-value>.001).

One-way ANOVA is also a correlational analysis, based on the correlational coefficient between variables. The ANOVA analysis comes up with the exact same p-value as the t-test (.003); however, it uses an f-test rather than t-test.

General linear regression gives substantially more information than a t-test or ANOVA. The parameter “gender” is significant ( a face one would know from the previous two tests); however, the regression allows to know the correlation between the two (negative) and the approximate effect of gender on tests.

Univariate Analysis

The average mark in algebra (dependent variable) is skewed, largely because of the decision to group the variables by grades rather than keeping the continuous scores- a large number of students that failed (112) and earned a d, but the decision to model the variable in this way essentially puts high fails and low “d”s in the same category. The CTBS Math NCE score looks to be roughly normally distributed- based on the decision to keep it as a continuous score. The “school” variable is even distributed between school alpha and school beta. Finally, number of days absent is positively skewed: this is a function of numerous students not missing any days of school (0), and the distribution thinning as the number of absent days increases. Although there are some problems with this data, the regression is generally robust.

Looking at the results, all of the parameters are significant, and most of the results make intuitive sense: an increase in the number of days absent leads to a lower algebra score; grades in the CTBS and mark in spring math are positively correlated with the score in algebra; finally, depending on the school chosen, there is a negative correlation. Looking at the effect size, the mark in spring math is a strong positive predictor; and school a strong negative predictor.

The difference between unstandardized coefficients and standardized coefficients is the use of scale: standardized coefficients are corrected for scale. The main difference between the two are the strong negative predictor (number of days absent) and the strong positive predictor (CTBS Math Percentile). Finally, school is less important once scaled to the other variables

I chose to add on the model above to understand how variables that look at English grades and bilingual status might also predict math grades. The intuition behind this inclusion is that individuals that don’t understand English may not understand what the math instructor is saying; or may also not ask needed questions due to a perceived obstacle in communication with the teacher.

Model= Algebra Scores (DV)= Mark in English (IV)+ CTBS Math Score (IV)+ CTBS Language NCE Score (IV) + Bilingual status (IV)+ Proficiency in native language (IV)+ Number of days absent

Overall, this model has a significantly higher adjusted r-squared than the previous model- this is important because the regular r-squared will increase regardless of whether the variable is significant or not. My hypothesis that language plays a role in math scores had a mixed result: “Mark in English 95” was a significant positive predictor of the algebra score; this could be because it is capturing that good students do well, or it could be that those with better English ability can understand math better. “Proficiency in native language” was also a significant positive predictor leading one to believe that language ability plays some type of role in understanding math. The other two variables, “CTBS language score” and “Bilingual Status” were not significant in predicting the algebra score.