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Shtirlitz [24]
2 years ago
13

A mathematics teacher wanted to see the correlation between test scores and

Mathematics
1 answer:
SpyIntel [72]2 years ago
8 0

Answer:

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:

y=a+bx

Here,

<em>y</em> = dependent variable = test grade

<em>x</em> = independent variable = homework grade

<em>a</em> = intercept

<em>b</em> = slope

Compute the value of <em>a</em> and <em>b</em> as follows:

a=\frac{\sum Y\cdot \sum X^{2}-\sum X\cdot\sum XY}{n\cdot \sum X^{2}-(\sum X)^{2}}\\\\=\frac{(592\times 44909)-(591\times45227)}{(8\times44909)-(591)^{2}}\\\\=-14.316                b=\frac{n\cdot \sum XY-\sum X\cdot\sum Y}{n\cdot \sum X^{2}-(\sum X)^{2}}\\\\=\frac{(8\times 45227)-(591\592)}{(8\times44909)-(591)^{2}}\\\\=1.195

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

y=-14.316+1.195x

Compute the value of <em>x</em> for <em>y</em> = 68 as follows:

y=-14.316+1.195x

68=-14.316+1.195x\\1.195x=68+14.316\\1.195x=82.316\\x=68.884\\x\approx 69

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

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