Question

School administrators wondered whether class size and grade achievement (in percent) were related. A random sample of classes revealed the following data:  

No. Students (x) 15 10 8 20 18 6

Avg. grade (%) (y) 85 90 82 80 84 92

Use a significance level of .05 to test the claim that the two variables (no. students and avg grade) are linearly related.

Based on your analysis, what is the best predicted avg grade for a class size of 12 ? Round your answer to one decimal place (i.e. one digit to the right of the decimal place)

Answer 1

Running, a linear regression model on the given data, by regressing Avg. grade on No. of Students, using excel:

To test:

H0: The fitted model is same as the intercept only model i.e. the two variables share no causal relationship

Ha: The fitted model is significantly different from the intercept only model i.e. the two variables share a linear significant causal relationship

From the F statistic and the corresponding p-value obtained for the overall model, F = 3.313, p-value = 0.143 > 0.05, we fail to reject the null hypothesis at 5% level. We may conclude that the data does not provide sufficient evidence to support the claim that the two variables (no. students and avg grade) are linearly related.

For x = 12,

Predicted grade = 92.562 - 0.55 (12)

= 85.962 = 86.0 (apprx.)

However, since the fitted model is not that efficient in predicting grades, the above result obtained would not be that reliable.