Question

A study of 427 college students was conducted to test whether high school GPA is a predictor of first-year college GPA. school GPA are expected to do better in college. Students with higher High colgpa-Grade point average in college (Range 0.85 -3.97) hsgpaHigh school GPA (Range 2.29-4.5) Model 1: OLS, N-427 Dependent variable: colgpa coefficient std. error const hsgpa 0.5 0.15 R-squared: 0.854880 a. (3%) Write the equation for the least-squares regression line: y- b. (396) The null hypothesis is: ß (pick one: 0 C. (396) Calculate the t-ratio- d. (396) The critical value for the t distribution ( -0.05 and d N-2 ) is (396) Can we reject the null hypothesis? (pick one) yes no e.

Answer 1

a) The least square regression line is :

$\hat{y} = 1 + 0.5hsgpa$

b) The null hypothesis is $H_0:\beta = 0$

c) The value of the test statistic $t = \frac{\hat{\beta }}{SE(\hat{\beta })} = \frac{0.5}{0.15} = 3.3333$

d) critical value for t distribution = $t_{0.05,425} = 1.96556$

e) Since t statistic > critical value, so we reject the null hypothesis.

ans-> yes