An attempt was made to construct a regression model...

An attempt was made to construct a regression model explaining student scores in intermediate economics courses (Waldauer, Duggal, and Williams 1992). The population regression model assumed that $Y=$ total student score in intermediate economics courses $X_1=$ mathematics score on Scholastic Aptitude Test $X_2=$ verbal score on Scholastic Aptitude Test $X_3=$ grade in college algebra $(A=4, B=3, C=2$, $D=1$ ) $X_4=$ grade in college principles of economics course $X_5=$ dummy variable taking the value 1 if the student is female and 0 if male $X_6=$ dummy variable taking the value 1 if the instructor is male and 0 if female $X_7=$ dummy variable taking the value 1 if the student and instructor are the same gender and 0 otherwise This model was fitted to data on 262 students. Next we report $t$-ratios, so that $t_j$ is the ratio of the estimate of $\beta_j$ to its associated estimated standard error. These ratios are as follows: $$ \begin{aligned} & t_1=4.69, t_2=2.89, t_3=0.46, t_4=4.90, \\ & t_5=0.13, t_6=-1.08, t_7=0.88 \end{aligned} $$ The objective of this study was to assess the impact of the gender of student and instructor on performance. Write a brief report outlining what has been learned about this issue.

An attempt was made to construct a regression model explaining student scores in intermediate economics courses (Waldauer, Duggal, and Williams 1992). The population regression model assumed that
$Y=$ total student score in intermediate economics courses
$X_1=$ mathematics score on Scholastic Aptitude Test
$X_2=$ verbal score on Scholastic Aptitude Test
$X_3=$ grade in college algebra $(A=4, B=3, C=2$, $D=1$ )
$X_4=$ grade in college principles of economics course
$X_5=$ dummy variable taking the value 1 if the student is female and 0 if male
$X_6=$ dummy variable taking the value 1 if the instructor is male and 0 if female
$X_7=$ dummy variable taking the value 1 if the student and instructor are the same gender and 0 otherwise
This model was fitted to data on 262 students. Next we report $t$-ratios, so that $t_j$ is the ratio of the estimate of $\beta_j$ to its associated estimated standard error. These ratios are as follows:
$$
\begin{aligned}
& t_1=4.69, t_2=2.89, t_3=0.46, t_4=4.90, \\
& t_5=0.13, t_6=-1.08, t_7=0.88
\end{aligned}
$$
The objective of this study was to assess the impact of the gender of student and instructor on performance. Write a brief report outlining what has been learned about this issue.

Key Concepts

Multiple Linear Regression

Multiple linear regression is a statistical technique used to model the relationship between one dependent variable and several independent variables. It allows researchers to estimate the effect of each predictor while controlling for the influence of others, making it a powerful tool for understanding complex phenomena in various fields.

Dummy Variable Coding

Dummy variable coding is a method used in regression analysis to incorporate categorical variables. By assigning values such as 0 or 1 to represent different categories, it allows for the inclusion of qualitative data (e.g., gender) in models that primarily use quantitative inputs.

t-Statistic in Regression Analysis

The t-statistic in regression analysis is used to test whether an estimated regression coefficient significantly differs from zero. It is calculated as the ratio of the estimated coefficient to its standard error, serving as the basis for hypothesis tests regarding the impact of individual predictors on the dependent variable.

Hypothesis Testing of Regression Coefficients

Hypothesis testing of regression coefficients involves assessing whether each independent variable has a statistically significant effect on the dependent variable. This is typically done using the t-statistic to determine if the observed relationship could have occurred by chance or if it is likely to be a true effect in the population.

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