2. ] Suppose you conducted a study on standardized tests scores from students in
ID: 3297685 • Letter: 2
Question
2. ] Suppose you conducted a study on standardized tests scores from students in 3 majors (psychology, finance, and engineering). You sample 150 students and record their major and test score. You also believe that anxiety seriously compromises performance, so you record mean blood pressure for each student during the test. You want to determine if the majors performed differently on the standardized test, after adjusting for test-taker anxiety.
a. What kind of model is this? What are the dependent variable, independent variable, and covariate(s)?
b. Write the model in mathematical notation eg. y = B0 + B1 *x1 ...
Define all the terms you use, what each coefficient represents.
Coefficients
Estimate
Std. Error
t-statistic
p-value
Intercept
7.6760
6.7602
1.135
0.2995
Book Sales
0.8285
0.5394
1.536
0.1754
Production Cost
3.6616
1.1178
3.276
0.0169
Promotional Cost
7.6211
1.6573
4.598
0.0037
Adjusted R-Squared
0.95
Extra Credit: In question 1, the adjusted R-squared value is 0.95. Suppose you excluded Book Sales from the model and reran it. What do you think would happen to the R-squared value? Justify your answer.
Coefficients
Estimate
Std. Error
t-statistic
p-value
Intercept
7.6760
6.7602
1.135
0.2995
Book Sales
0.8285
0.5394
1.536
0.1754
Production Cost
3.6616
1.1178
3.276
0.0169
Promotional Cost
7.6211
1.6573
4.598
0.0037
Adjusted R-Squared
0.95
Explanation / Answer
a. What kind of model is this? What are the dependent variable, independent variable, and covariate(s)?
This is a multiple regression model in which the dependent variable is standardized tests scores
and the independent variables are mean blood pressure during the test and Majors.
b.
The model in mathematical notation is,
TestScore = B0 + B1 * MeanBloodPressure + B2 * Major_F + B3 * Major_E
where TestScore is the standardized test score.
MeanBloodPressure is Mean Blood Pressure during the test
Major_F = Major_E = 0 when major is psychology
Major_F = 1 and Major_E = 0 when major is finance
Major_F = 0 and Major_E = 1 when major is engineering.
B0 represent the Test Score when the MeanBloodPressure is 0 and major is psychology.
B1 represent unit change in TestScore when there is unit change in mean blood pressure
B2 represent change in TestScore when major is finance and mean blood pressure is constant.
B3 represent change in TestScore when major is engineering and mean blood pressure is constant.
The p-value for the coefficient of Book Sales is 0.1754 (greater than 0.05), which suggests that Book Store is not significant in determining the dependent variable.
So, if we exclude Book Sales from the model , we are removing an insignificant variable and this will increase adjusted R-squared value.
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