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:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.