A teacher believes that the third homework assignment is a key predictor in how

Question

A teacher believes that the third homework assignment is a key predictor in how well students will do on the midterm. Let x represent the third homework score and y the midterm exam score. A random sample of last terms students were selected and their grades are shown below. Assume scores are normally distributed. HW3 Midterm 56.384 8.4 41.096 20.2 56.088 21.1 17.3 54.912 18.1 56.064 15.8 47.752 15.1 46.744 41 56.704 49.872 13.8 8.9 37.816 49.04 16 18.1 55.064 13.9 42.016 12.4 47.856 7.8 37.232 39.36 6.5 -6268 7.7 40.088 6.9 39.936 19.1 50.504 48.6 39.224 15 7.1 22 59,68

Explanation / Answer

a) Correlation coefficient r = 0.9400
b)P-value = 0.0000
c)P-value is very small (0.0000) therefore correlation is statistically significant at the 0.05 significance level.
d)Regression equation is,
y^ = 29.2993 + 1.3069 * HW3
e) At HW3=19.3,
Exam score = y^ = 29.2993 + 1.3069 * 19.3 =54.5231
f)
Interpritation of Slope Coefficient-
For each additional point on homework 3, the predicted midterm grade will increase 1.3069 points.

HW3 Midterm 21.1 56.384 SUMMARY OUTPUT 8.4 41.096 20.2 56.088 Regression Statistics 17.3 54.912 Multiple R 0.94003 Correlation Coefficient 18.1 56.064 R Square 0.883655 15.8 47.752 Adjusted R Square 0.878114 15.1 46.744 Standard Error 2.700606 24.1 56.704 Observations 23 13.8 49.872 8.9 37.816 ANOVA 16 49.04 df SS MS F Significance F 18.1 55.064 Regression 1 1163.256 1163.256 159.4971 2.82E-11 P-value 13.9 42.016 Residual 21 153.1588 7.293275 12.4 47.856 Total 22 1316.415 7.8 37.232 6.5 39.36 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% 22 62.68 Intercept 29.2993 1.618734 18.1001 2.73E-14 25.93292 32.6656 25.93292 32.6656 7.7 40.088 X Variable 1 1.3069 0.103485 12.62922 2.82E-11 1.091726 1.522144 1.091726 1.522144 6.9 39.936 19.1 50.504 15 48.6 7.1 39.224 22 59.68

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