Slope is rise over run. Go up 1 unit, right 4 units to get to the next point.
the slope is 1/4
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](https://tex.z-dn.net/?f=y%3Da%2Bbx)
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:
![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](https://tex.z-dn.net/?f=b%3D%5Cfrac%7Bn%5Ccdot%20%5Csum%20XY-%5Csum%20X%5Ccdot%5Csum%20Y%7D%7Bn%5Ccdot%20%5Csum%20X%5E%7B2%7D-%28%5Csum%20X%29%5E%7B2%7D%7D%5C%5C%5C%5C%3D%5Cfrac%7B%288%5Ctimes%2045227%29-%28591%5C592%29%7D%7B%288%5Ctimes44909%29-%28591%29%5E%7B2%7D%7D%5C%5C%5C%5C%3D1.195)
The linear regression equation that represents the set of data is:
![y=-14.316+1.195x](https://tex.z-dn.net/?f=y%3D-14.316%2B1.195x)
Compute the value of <em>x</em> for <em>y</em> = 68 as follows:
![y=-14.316+1.195x](https://tex.z-dn.net/?f=y%3D-14.316%2B1.195x)
![68=-14.316+1.195x\\1.195x=68+14.316\\1.195x=82.316\\x=68.884\\x\approx 69](https://tex.z-dn.net/?f=68%3D-14.316%2B1.195x%5C%5C1.195x%3D68%2B14.316%5C%5C1.195x%3D82.316%5C%5Cx%3D68.884%5C%5Cx%5Capprox%2069)
Thus, the homework grade, to the nearest integer, for a student with a test grade of 68 is 69.