A Interpret the slope of the leastsquares regression line B

A. Interpret the slope of the least-squares regression line.

B. Given that sx = 1.5751 and sy = 8.6415, calculate the correlation, r.

C. Use your answer from part (B) and calculate r². Interpret this value.

D. One student was absent on the day of the test. He studied for 6 hours and scored a 70 on the test. What effects, if any, does this point have on the least-squares linear-squares line and correlation? Explain

Solution

A.) For every hour a student studies his test grade increases by 4.1830.

B.) Slope = 4.1830

sxy/sxx = 4.1830

sxy = 4.1830 × 1.5751^2 = 10.3778

r = sxy /(sx × sy)

= 10.3778/(1.5751 × 8.6415)

= 0.7624

C.) r2 = 0.7624^2 = 0.5813

58.13% of the variation in test grade is explained by the number of hours studied.

D.) If a student studies for 6 hrs his test grade would be

Test grade = 73.7788 + (4.1830 × 6) = 98.88

Therefore the student scores less than what he would have scored otherwise.