Question

A statistics professor would like to build a model relating student scores on the first test to the scores on the second test. The test scores from a random sample of 21 students who have previously taken the course are given in the table...

a) Regression model parameters cannot be estimated with this data
b) First Test Grade=β0+β1(Second Test Grade)+εi
c) Second Test Grade=β0+β1(First Test Grade)+εi
d) There is not enough information to estimate the parameters

Answer 1

In statistics, a regression model can estimate the relationship between test scores; with 21 student scores, parameters can be calculated, specifically using the second test score as a dependent variable and the first test score as an independent variable.

Step-by-step explanation:

The question is regarding a statistical analysis where a regression model is to be built relating student scores on the first test to scores on the second test. Given that data from a random sample of 21 students is available, it is possible to estimate the parameters for the regression model. The correct form for the regression equation, in this case, should be Second Test Grade = β0 + β1(First Test Grade) + εi, where the first test grade is the independent variable (predictor) and the second test grade is the dependent variable (outcome). Concluding statements about whether the regression model can be used to predict the dependent variable are typically made after the regression parameters (β0 and β1) have been estimated and tested for significance, often with additional supporting evidence such as a correlation coefficient or scatter plot analysis.