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 coefficient to the nearest tenth. using this equation, estimate the homework grade to the nearest integer for a student with a test grade of 32

To find the linear regression equation, we need to calculate the slope and y-intercept using the given data points. The equation for a linear regression line is in the form y = mx + b, where m represents the slope and b represents the y-intercept.

Let's start by calculating the slope (m). The slope is given by the formula:

m = (Σ(xy) - (Σx)(Σy) / n(Σx^2) - (Σx)^2)

where Σ represents the sum, xy represents the product of x and y for each data point, Σx represents the sum of x values, Σy represents the sum of y values, and Σx^2 represents the sum of squared x values.

In this case, the given data points are:

x (homework grade): 85, 92, 78, 89, 94

y (test grade): 90, 87, 75, 92, 88

Let's calculate the necessary sums:

Σxy = (85 * 90) + (92 * 87) + (78 * 75) + (89 * 92) + (94 * 88)

Σx = 85 + 92 + 78 + 89 + 94

Σy = 90 + 87 + 75 + 92 + 88

Σx^2 = (85^2) + (92^2) + (78^2) + (89^2) + (94^2)

Now we can substitute these values into the slope formula:

m = (Σ(xy) - (Σx)(Σy)) / (n(Σx^2) - (Σx)^2)

Once we calculate the slope, we can move on to finding the y-intercept (b). The y-intercept is given by the formula:

b = (Σy - m(Σx)) / n

After finding both the slope and the y-intercept, we can write the linear regression equation y = mx + b.

Lastly, we can use this equation to estimate the homework grade (x) for a student with a test grade of 32. Simply substitute the given test grade (32) into the equation and round the result to the nearest integer.

I hope this helps :D