Question

In: Statistics and Probability

The following are the average scores on the mathematics part of the Scholastic Aptitude Test (SAT)...

The following are the average scores on the mathematics part of the Scholastic Aptitude Test (SAT) for some of the years from 1994 to 2009.

Year, SAT Score

1994 504

1996 508

1998 512

2000 514

2002 516

2004 518

2005 520

2007 515

2009 515

Assuming a simple linear regression model, predict the average scores in 1997, 2006 and 2008

Solutions

Expert Solution

Following is the output of regression analysis:

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.799131184
R Square 0.63861065
Adjusted R Square 0.5869836
Standard Error 3.182824921
Observations 9
ANOVA
df SS MS F Significance F
Regression 1 125.3096009 125.3096009 12.36969088 0.00976622
Residual 7 70.91262136 10.13037448
Total 8 196.2222222
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept -1047.614887 443.8867047 -2.360095213 0.050334237 -2097.240153 2.010379887
Year, X 0.779935275 0.22175792 3.517057134 0.00976622 0.255561119 1.304309431

The simple linear regression analysis is:

y' = -1047.61+0.78x

The predicted value for x = 1997 is

y' = -1047.61+0.78*1997 =  510.05

The predicted value for x = 2006 is

y' = -1047.61+0.78*2006 =  517.07

The predicted value for x = 2008 is

y' = -1047.61+0.78*2008 =  518.63

orchestra answered 2 years ago
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