A nameless math instructor wishes to estimate a linear equation that relates qui

Question

A nameless math instructor wishes to estimate a linear equation that relates quiz average and test average percentages after administering the 1" Unit Exam. The following data represents the quiz average earned and test average achieved by twenty-seven students in a College Algebra class. Using Microsoft Excel or a Graphing Calculator, create a scatter/stat plot of the data to answer the questions below. BE SURE TO ENTER DATA CORRECTLY. HOWEVER, DO NOT ENTER INCOMPLETE DATA. (ie. Student 20) Test Average Quiz Average Percentage 99.09 96.36 94.55 93.64 92.73 Percentage Student 1 Student 2 Student 3 Student4 Student 5 Student 6 Student 7 Student 8 Student 9 Student 10 Student 11 Student 12 Student 13 Student 14 Student 15 Student 16 Student 17 Student 18 Student 19 Student 20 97 85 91 83 81 61 75 90 87 90.91 90 90 89.09 89.09 89.09 82.73 81.82 80.91 80 79.09 73.64 69.09 69.09 69.09 67 86 70 29 67.27 66.36 43 51 30 64 87 0 40 Student 21 Student 22 Student 23 Student 24 Student 25 Student 26 Student 27 63.64 62.73 53.64 43.64 27.27

Explanation / Answer

a) ## Using Minitab

Regression Analysis: Test versus Quiz

The regression equation is
Test = - 8.2 + 0.973 Quiz

Predictor Coef SE Coef T P
Constant -8.25 15.55 -0.53 0.601
Quiz 0.9727 0.1959 4.96 0.000

S = 17.0804 R-Sq = 50.7% R-Sq(adj) = 48.6%

Analysis of Variance

Source DF SS MS F P
Regression 1 7191.6 7191.6 24.65 0.000
Residual Error 24 7001.7 291.7
Total 25 14193.4

b) When the quize average score is 73% The Average test percentage is

Test = - 8.2 + 0.973 Quiz

Test = - 8.2 + 0.973*73

= 62.82.

Hence The Average test percentage 63%

c) The average quize percentage when the average test percentage is 85% is given by

Test = - 8.2 + 0.973 Quiz

85 +8.2 =0.973*Quiz

Quiz= 95.79

There The average quize percentage is 96%.

d)

c. As quize average increases, the test average increase.

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