A mathematics teacher wanted to see the correlation between test scores and
homework. The homework grade (x) and test grade (y) are given in the accompanying
table. Write the linear regression equation that represents this set of data, rounding
all coefficients to the nearest hundredth. Using this equation, estimate the homework
grade, to the nearest integer, for a student with a test grade of 68.
Homework Grade (x) Test Grade (y)
X | Y
88 | 90
55 | 55
89 | 91
85 | 88
61 | 52
76 | 76
76 | 81
61 | 59

The linear regression equation which models the relationship between homework grade and test grade and the predicted homework grade are :

Using technology, the linear model can be obtained using either excel or a linear regression calculator.

Using a linear regression calculator which gives the linear equation in the form :

y = 1.20x - 14.32

Using the model equation obtained :

y = 1.20x - 14.32

68 = 1.20x - 14.32

68 + 14.32 = 1.20x

82.32 = 1.20x

x = (82.32 ÷ 1.20)

x = 68.6

x = 69 (nearest integer)

Therefore, the estimated homework grade for a test score of 68 is 69

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The homework  grade, to the nearest integer, for a student with a test grade of 68 is 69.

Step-by-step explanation:

The general form of the linear regression equation is:

Here,

y = dependent variable = test grade

x = independent variable = homework grade

a = intercept

b = slope

Compute the value of a and b as follows:

The linear regression equation that represents the set of data is:

Compute the value of x for y = 68 as follows:

Thus, the homework  grade, to the nearest integer, for a student with a test grade of 68 is 69.

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step-by-step explanation: