STAT-2509 - Two Freshmen Algebra Classes at McNair Academic High School - Statistics Assignment Help

Assignment Task

Two freshmen algebra classes at McNair Academic High School in Jersey City, New Jersey were studied. One of which used laptop computers at school and at home, while the other class did not. In each class, students were given a survey at the beginning and end of the semester, measuring his/her technological level. The scores were recorded for the end of semester survey ( X ) and the final examination (Y ) for the laptop group. The data are recorded in the table below: Student End of Term Survey Score ( X ) Final Exam Grade (Y )
 1 100 98
 2 96 97
 3 88 88
 4 100 100
 5 100 100
 6 96 78
 7 80 68
 8 68 47
 9 92 90
 10 96 94
 11 88 84
 12 92 93
 13 68 57
 14 84 84
 15 84 81
 16 88 83
 17 72 84
 18 88 93
 19 72 57
 20 88 83 

(a) Plot a scatter diagram (using SAS, see part (i) of the SAS class example) to get an idea of the form of the relationship between the ‘end of term survey’ score and the ‘final exam’ grade. Does the scatter diagram indicate an approximately straight line?

(b) State a SLR model making sure you give all assumptions necessary for statistical inference.

(c) Find the least squares estimates of 0 and 1 . Find the least squares fitted regression line.

2. Refers to question 1. (a) Find a 95% Confidence Interval for the mean value of the response variable (i.e. of the ‘final exam’ grade) and a 95% Prediction Interval for an individual value of this response variable when the value of ‘end of term survey’ score is 99 (i.e. p x = 99). What is your conclusion about the widths of these two intervals? (b) Use SAS to answer (a) and compare your SAS results to your hand calculated results. (See part (c) of the SAS class example.)

3. Refers to question 1. Perform a residual analysis using SAS (see part (b) of the SAS class example). What can you say about the model?

4. Refers to question 1. (a) Perform the Lack-of-Fit test to find out if we can use the ‘end of term survey’ score to predict the ‘final exam’ grade. Use ? = 0.05. (b) Use SAS (proc reg statement with model y-variable = x-variable/lackfit;) to verify your results in part (a).

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