Information about least-squares regression

Reference no: EM1396358

A nationwide standardized test taken by high school juniors and seniors may or may not measure academic potential, but we can nonetheless examine the relationship bewteen scores on such test and performance in college.

We have chosen a random sample of 95 students just finishing their first year of college, and for each student we've recorded their score on one such standardized test and their grade point average for their first year in college. For our data, the least-squares regression equation relating the two variables score on this standardized test (denoted by x and ranging from 400 to 1600) and first-year college grade point average (deonted by y and ranging from 0 to 4) is ^y=0.8888 + 0.0019x. The standard error of the slope of this least-squares regression line is approximately 0.0009.

Based on these sample results, test for a significant linear relationship between the two variables by doing a hypothesis test regarding the population slope. (Assume that the variable y follows a normal distribution for each value of x and that the other regression assumptions are satisfied.) Use the 0.10 level of significance, and perform a two-tailed test.

Complete the following questions:

1) The null hypothesis

2) The alternative hypothesis

3) The type of test statistic

4) The value of the test statistic (round to at least 3 decimal places)

5) The p-value (round to at least 3 decimal places)

6) Based on the sample results, can we conclude (using the 0.10 level) that there is a significant linear relationship between score on the standardized test and first-year college grade point average. Yes or No

Reference no: EM1396358

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