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...

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 2 3 -3 Y -12 -8 9 1 -5 -6 -1 4 7 -8

Asked on by btstjos

1 Answer | Add Yours

violy's profile pic

violy | High School Teacher | (Level 1) Associate Educator

Posted on

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:) 

We’ve answered 318,912 questions. We can answer yours, too.

Ask a question