In a particular college math class, students begin the semester taking a pre-tes
ID: 3160605 • Letter: I
Question
In a particular college math class, students begin the semester taking a pre-test (Pre). At the end of the semester, students receive a final class percentage (Final). Both scores are recorded as percentages out of 100. It was desired to know if performance on the pre-test was predictive of final class percentage. There were 9 students in the class. The results are below: For all of the parts below (except for graphs), please perform the calculations by hand, and show your work. You may use R to check your answers. Make a scatterplot of the data. Does it seem like a straight line model is reasonable? Assuming a straight-line model, compute estimates of the intercept (beta_0) and slope (beta_1). Create a plot of the residuals vs fitted values and a QQ plot of the residuals. Do the necessary regression assumptions seem met? Perform a test of H_0: beta_1 = 0 vs. H_A: beta_1 notequalto 0, using a t-test at alpha = 0.05. Make a conclusion in the context of the problem. Compute R^2 for this regression. If a student scores 80 on the pre-test, what does the model predict will be their final score? Compute the SE of this estimate assuming it is for a single future value.Explanation / Answer
students Pre test Final
1 83 68
2 81 59
3 70 72
4 79 75
5 69 55
6 61 52
7 88 81
8 72 63
9 86 70
Scatter plot
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.71
R Square 0.50
Adjusted R Square 0.43
Standard Error 7.27
Observations 9.00
ANOVA
df SS MS F Significance F
Regression 1.00 366.92 366.92 6.94 0.03
Residual 7.00 369.97 52.85
Total 8.00 736.89
Coefficients Standard Error t Stat P-value
Intercept 8.60 21.96 0.39 0.71
X Variable 1 0.75 0.29 2.63 0.03
Regression Eqn is
Y = 8.6 + 0.75 X1(pre test)
Y at 80 = 8.6 + 0.75 X 80 = 68.6
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