Question

Estimate: GPA 50 + 61GRE + ε, where GRE is a student's score on the math portion of the Graduate Record Examination (GRE) score and GPA is the student's grade point average in graduate school. Click here for the Excel Data File Click here for the CSV Data File a. Use R's predict0 function to construct the 90% confidence interval for the expected GPA for an individual who scored 730 on the math portion of the GRE. (Round answers to 2 decimal places.) Confidence interval to b. Use R's predict() function to construct the 90% prediction interval for GPA for an individual who scored 730 on the math portion of the GRE. (Round answers to 2 decimal places.) Prediction interval to

Excel File

GPA	GRE
2.8	720
3.1	740
3.5	720
3.5	740
2.2	750
3.5	770
3.9	640
3.6	750
2.4	680
2.3	770
2.3	700
2.9	770
2.1	640
2.2	770
2.5	740
3	770
3.9	670
3.1	760
3.3	680
2.1	690
2.5	750
3.1	700
2.6	680
2.7	650

Answer 1

Using R,

R Console names (data) [1 "GPA" "GRE" Model-1m (GPA~GRE, data-data) Model Call: Im ( f rmula = GPA ~ GRE , data = data) Coefficients: (Intercept) GRE 3.3720123 -0.0006857 new.data-data.frame (GRE-730) > #To obtain a 90% confidence interval for expected GPA at sc re = 730 > predict (Model, newdatanew.data, intervalconfidence',level-0.90) fit upr 1 2.8714532.659692 3.083213 > #To obtain a 90% prediction interval for expected GPA at sc re = 730 > predict (M del, newdata = new. data, Interval = 'predicti n ', level=0.90) fit upr 1 2.8714531.845522 3.897383 2

Hence, from the above output,

The expected GPA when Score obtained is 730 is

2.871453

The 90% Confidence interval for expected GPA for an individual who scored 730 on the math portion of the GRE is

2.659692,3.083213)

The 90% Prediction interval for expected GPA for an individual who scored 730 on the math portion of the GRE is

1.845522,3.897383