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

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Regression Statistics

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Multiple R 0.919958

R Square 0.846322

Standard Error 71.57225

Observations 5

Anova

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DF SS MS F Sign. F

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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

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Coefficient Standard Lower Upper

s Error t Stat P-Value 95% 95%

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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

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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).

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.

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Q2: Regression equation :

ŷ = -133.5681 + (8.1377) x

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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

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Q4: Test statistic:

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