Question

Suppose you want to study the effects of the number of students per classroom in algebra courses and students’ performance in algebra courses for high schools in Kansas. You collected a random sample and now you have data for the above two variables. You called them as number students (which refers to the number of students per classroom in algebra courses), and students performance (which refers to the students’ performance in algebra courses - measured as their final grade in a scale from 0 to 4). Therefore, you want to know how number students explains students performance

(a) What is the independent variable?

(b) What is the dependent variable?

(c) Using the variables names, write the simple linear regression model.

(d) Knowing that the OLS estimate for the intercept is 3.4, and for the slope is −0.02, write the estimated OLS regression line (or SRF) using the variables names.

(e) What is the predicted value for whichever is your dependent variable for a classroom with 20 students?

(f) What is the predicted effect on your dependent variable for each additional increment (i.e, when you increase one unit) of your independent variable?

Answer 1

a,b,c).

Consider the given problem here we want to study the effect of “numbers of students per class” on “students performance”. So, here the “independent variable” is “X=numbers of students” and the dependent variable is “average grade points” of all the students in to the class. Now, the simple linear regression equation is given by.

=> Y = b0 + b1*X + u, => Mean Grade Points = b0 + b1*Numbers of Students + u.

d).

Now, we have given that the “estimated value” of intercept and slope are “3.4” and “-0.02”. So, the estimated regression equation is given by, => Mean grade Points = 3.4 - 0.02*Numbers of Students.

e).

Now, if the numbers of students is “20”, =>”X=20”, => the average grade point of that class is given by.

=> Mean Grade Point = 3.4 - 0.02*20 = 3 > 0, => the “predicted value of mean grade point” is “3”.

f).

Now, the estimated regression model is given by, => Mean Grade Point = 3.4 - 0.02*Numbers of Students.

=> if the “Numbers of Students” increases by “1 unit”, => “Mean Grade Point” decreases by “0.02”. So, the predicted effect on the dependent variable is “0.02”.