an incoming student has a letter score = 8 and SAT = 1300 If this student decrea

Question

an incoming student has a letter score = 8 and SAT = 1300

If this student decreases his SAT by 150 points how much would the student's predicted college GPA change?

1 SUMMARY OUTPUT 3 Regression Statistics 4 Multiple R 0.57610736 5 R Square 0.33189969 6 Adjusted R S 0.31812443 7 Standard Err 0.61867935 8 Observations 100 10 ANOVA df F Significance F 2 18.4445539 9.22227694 24.0938899 3.1976E-09 MS 12 Regression 13 Residual 14 Total 15 16 17 Intercept 18 SAT 19 Letters 97 37.1281211 0.38276414 99 55.572675 Coefficients tandard Errot Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% 0.304349 0.335500180.90715 0.36657559 0.970224 0.361526-0.970224 0.361526 0.00161594 0.00029311 5.51311804 2.9121E-07 0.0010342 0.00219767 0.0010342 0.00219767 0.12428939 0.04260094 2.91752711 0.00438437 0.03973832 0.20884046 0.03973832 0.20884046

Explanation / Answer

Given that,

Letter score = 8

SAT = 1300

As per above given summary,

GPA= 0.00161594*SAT + 0.12428939*Letters -0.304349

GPA= 0.00161594*1300+ 0.12428939*8-0.304349

GPA1300  =2.790688

If SAT decrease by 150 points from 1300 points then updated SAT = 1150

thus GPA= 0.00161594*1150+ 0.12428939*8-0.304349

GPA1150  =2.548297

Hence, the student's predicted college GPA change =  GPA1150 - GPA1300  

= 2.548297 - 2.790688

= -0.242391

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