Question

Research into the relationship between hours of study and grades show widely different conclusions. A recent...

Research into the relationship between hours of study and grades show widely different conclusions. A recent survey of graduates who wrote the Graduate Management Admissions Test (GMAT) had the following results.

Hours Studied Average Score

(Midpoint)

64 350

72 450

79 550

106 650

99 750

The Excel output for this regression is as following

SUMMART OUTPUT

____________________________

   Regression Statistics

____________________________

Multiple R 0.919958

R Square 0.846322

Adjusted R Square 0.795097

Standard Error 71.57225

Observations 5

Anova

___________________________________________________________________________________________

   DF SS MS F Sign. F

___________________________________________________________________________________________

   84632.2 84632.2 16.521 0.0268

Regression. 1 4 4 4 6

   15367.7 5112.58

Residual 3 6 7

Total 4 100000

___________________________________________________________________________________________

   Coefficient Standard Lower Upper

   s Error t Stat P-Value 95% 95%

___________________________________________________________________________________________

   171.192 0.4921 411.24

Intercept -133.568 8 -0.78022 6 -678.38% 4

   0.0268

X Variable 1 8.137715 2.00207 xxxxxx 6 1.7662 14.509

___________________________________________________________________________________________

a) How accurate is this regression at predicting GMAT scores base on hours studied? Explain.

b) What is the regression equation for this relationship?

c) Use the regression equation to predict the average score for each category of hours studies.

d) Calculate the t statistic to determine approximately how “significant” this regression is (note that the t may be greater than or less than the value from the t table).

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

Q1: From ANOVA table p- value = 0.0268

Since p-value is less than 0.05,we reject the null hypothesis and can say that the regression model is significant to predict the GMAT scores.

Coefficient of determination, r2 = 0.8463

So about 84.63% variation in the response variable GMAT score explained by predictor variable hours studied.

--

Q2: Regression equation :

ŷ = -133.5681 + (8.1377) x

--

Q3:

X Y Predicted score, ŷ
64 350 -133.5681 + (8.1377) * 64 = 387.2457
72 450 -133.5681 + (8.1377) * 72 = 452.3474
79 550 -133.5681 + (8.1377) * 79 = 509.3114
106 650 -133.5681 + (8.1377) * 106 = 729.0297
99 750 -133.5681 + (8.1377) * 99 = 672.0657

--

Q4: Test statistic:

t = b /se(b1) = 8.137715/ 2.00207 = 4.0647

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