Question

6. Interpreting statistical software output in regression Aa Aa Suppose you work in the admissions department of a small liberal arts college. You wonder if you can predict students' college grade point averages (GPAs) by their SAT scores. You randomly select 50 recent graduates and collect their SAT scores and college GPAs. You use a statistical software package to run a regression predicting college GPA from SAT score. Use the following output to answer the questions that follovw Descriptive Statistics Mean 3.064 1816 Std Deviation 0.5574 280.20 College GPA SAT score 50 50 Model Summary Adjusted R Square 0.0884 Std Error of the Estimate 0.5322 Model R Square 0.327a 0.107 a. Predictors (constant): SAT score ANOVAa Sum of Squares Model df Mean Square 1.6295 0.28324 Two-Tailed Sig 0.0204b 1 Regression 1.6295 13.596 15.225 5.7530 Residual Total a. Dependent variable: college GPA b. Independent variables (constant): SAT score 48 49 Coefficientsa Standardized Coefficients Beta Unstandardized Coefficients Model Std Error 0.4985 0.000271 Two-Tailed Sig 0.0004 0.0204 1 (Constant) 1.8821 3.7759 SAT score 0.000651 0.327 2.3985 a. Dependent variable: college GPA , where Ý is the predicted value of The regression equation is Y- and X is the value of The Pearson correlation between SAT score and college GPA is You believe there is a linear relationship between SAT score and college GPA. You conduct a hypothesis test with the null hypothesis Ho: β1 = 0 versus the alternative hypothesis H1: β1キ0. Based on these results, with a significance level of a.05, you are linearly related reject the null hypothesis. You conclude that SAT score and college GPA

Answer 1

Ans:

Regression equation is:

Y'=0.000651 X+1.8821

Where Y' is the predicted value of college GPA and X is the value of SAT score.

Correlation between college GPA and SAT score is 0.327

Test statistic:

t=2.3985

p-value=0.0204

As,p-value<0.05,we should reject the null hypothesis.

You can conclude that SAT score and college GPA are linearly related.