Below are the data for the final scores (FINAL) in a sophomore statistics class.

Question

Below are the data for the final scores (FINAL) in a sophomore statistics class. Also included are the student scores on the math portion of the SAT (MSAT).

FINAL             72        79        65        89        95        78        75        73

MSAT             475     550     450     600     610     500     490     480

X = 4155     Y =626                     XY =329040           X2=2183225           Y2=49634

5.Calculate and interpret the coefficient of determination.

6. Test whether or not the slope coefficient differs from zero. Use alpha = 0.05.

7. Test whether or not the MODEL has explanatory power. Use alpha = 0.05. This should be a GLOBAL test.

8. What is the residual for the last observation in the data set?

9. What is the numerical value of Se?

10. What are the point estimates of and of 1?

Explanation / Answer

5) coefficient of determination = 0.9338 (rounded to four decimal places)

IT means 93.38% of variation in y can be explained by the variation in x

6) Since P values of xvariable is less than 0.05, we conclude that  slope coefficient differs from zero

7) Since R^2 square is so close to 1, we conclude that Model has explanatory power

8) Predicted value for last observation = 48.15819861+6.021939954*73 = 488 (nearest integer)

Residual = 480-488 = -8

9) Numerical value of Se is 16.676  (rounded to three decimal places)

10) Point estimate of = 0.9664 (rounded to four decimal places)

Point estimate of  1 = 6.02 (rounded to two decimal places)

SUMMARY OUTPUT Regression Statistics Multiple R 0.96635637 R Square 0.933844635 Adjusted R Square 0.92281874 Standard Error 16.67614242 Observations 8 ANOVA df SS MS F Significance F Regression 1 23553.31 23553.31 84.69559 9.28E-05 Residual 6 1668.562 278.0937 Total 7 25221.88 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 48.15819861 51.54074 0.934371 0.386173 -77.9575 174.2738 -77.9575 174.2738 X Variable 1 6.021939954 0.654344 9.203021 9.28E-05 4.420818 7.623062 4.420818 7.623062

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