You are interested in finding out if a student’s ACT score is a good predictor o

Question

You are interested in finding out if a student’s ACT score is a good predictor of their final college grade point average (GPA). You have obtained the following data and are going to conduct a regression analysis. Follow instructions on page 244 of your textbook under line of best fit to conduct this analysis? ACT GPA 22.0 3.0 32.0 3.78 33.0 3.68 21.0 2.94 27.0 3.38 25.0 3.21 30.0 3.65 a) What is the R? What type of relationship does it indicate (strong/weak; positive/negative)? b) Go to the coefficients readout. The constant is the intercept. Under that is the ACT and that is the slope. Using the straight line formula of Y = mx + b, which you will find on page 262, you will now predict some future GPA scores: In the formula (m) is the slope; (x) is the variable that you are looking to use as a predictor; and (b) is the intercept. Predict GPA from the following ACT scores using the regression equation/straight line formula (show all your work): 1) 20 2) 25 3) 34

Explanation / Answer

Ans:

a)Correlation cofficient,r=0.984

ACT and GPA are postively correlated and have strong correlation.

b)slope=r*sy/sx

slope,m=0.984*0.339/4.741=0.07

y-intercept,b=(3.377-0.07*27.143)=1.467

Regression line,y=mx+b

y=0.070x+1.467

when x=20

y=0.07*20+1.467=2.867

when x=25

y=0.07*25+1.467=3.217

when x=34

y=0.07*34+1.467=3.847

ACT GPA 1 22 3 2 32 3.78 3 33 3.68 4 21 2.94 5 27 3.38 6 25 3.21 7 30 3.65 mean= 27.143 3.377 std.dev= 4.741 0.339 corr. Coff.,r 0.984 slope,m= 0.070 y-intercept,b= 1.467

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