19  4.2 Exercises

The following dataset contains (fictitious) data about student scores in a class:

Student_ID Section Exam_1_Grade Exam_2_Grade Letter_Grade
1 Section 01 77.46055 76.72860 C
2 Section 01 76.70605 93.56616 A
3 Section 01 79.19778 73.79078 C
4 Section 01 78.22517 89.17746 B
5 Section 01 75.61382 79.87594 C
6 Section 01 81.70957 82.47253 B

19.1 Exercises 4.2.1

The following gives the results of a Least-Squares Regression predicting the Exam 2 scores from Exam 2 scores.


Call:
lm(formula = Exam_2_Grade ~ Exam_1_Grade, data = dat)

Residuals:
     Min       1Q   Median       3Q      Max 
-14.5503  -6.4976  -0.2267   7.2063  14.6106 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)   -1.7252    24.0995  -0.072 0.943077    
Exam_1_Grade   1.0829     0.3035   3.568 0.000559 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 8.621 on 98 degrees of freedom
Multiple R-squared:  0.115, Adjusted R-squared:  0.1059 
F-statistic: 12.73 on 1 and 98 DF,  p-value: 0.0005591

  1. State the null and alternate hypotheses of this ANOVA test.

  2. Interpret the intercept.

  3. Interpret the slope.

  4. Interpret the R-Squared value

  5. Report the test statistic and p-value, and state your conclusion from these.

  6. What grade would you predict on Exam 2 for someone who scored 80 on Exam 1?

19.2 Exercises 4.2.2

Here is a tabyl of the letter grades by section:

 Letter_Grade Section 01 Section 02
            A         18         13
            B         16         18
            C         14         15
            D          3          3

The following gives the results of a Chi-Square test to see if letter grades are different in the two sections:


    Pearson's Chi-squared test

data:  tabyl(dat, Letter_Grade, Section)
X-squared = 0.91895, df = 3, p-value = 0.8209

Report all steps of the hypothesis test.