# 1. Find the equation of the regression line for the given data. What is the predicted value of Y when X = -2? What is the predicted value of Y when X = 4? X -7 -2 5 1 -1 -2 0...

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We will use the form y = a + bx, and the following formulas:

a =[ (summation of y)(summation of x^2) - (summation of x)(summation of xy)]/[n(summation of x^2) - (summation of x)^2].

b = [n((summation of xy)-(summation of x)(summation of y)]/[n(summation of x^2) - (summation of x)^2].

where a is the y' intercept and b is the slope of the line.

We can use excel in calculating this. Input the values of x on the first column, and the values of y on teh second column.

FOr the summation of x. click a cell then, type =sum( . And then, click the first cell for x, and drag up to the last cell. Smae process

For the summation of y (just click teh first cell for y, and last cell for y).

For the summation of xy, we input = sumproduct, then click the

first cell of x and drag up to the last cell, then input (, )(comma).

Then, click the first cell for y, then, drag up to the last cell. FOr the sum of x^2, we input =sumsq( then click the first cell for x, drag up to the last cell. Same process for sum of y^2.

Using the process above, we will have:

summation of x = -4, summation of y = -19,

summation of xy = 216, summation of x^2 = 106, and summation of y^2 = 481, and n = 10 (number of data).

Applying the formula:

a = (-19(106)-(-4)(216))/(10(106)-(-4)^2) = -1.102.

b = (10(216)-(-4)(-19))/(10(106)-(-4)^2) = 1.996.

Hence, regression line is **y = -1.102 + 1.996x**.

For the predicted value of y, when x = -2:

y = -1.102 + 1.996(-2) =** -5.094**

For the predicted value of y when x = 4:

y = -1.102 + 1.996(4) = **6.882**

That is it:)