Find the slope of the regression line for the following data. xy113231 We have written the regression line in the form y=b0+b1x. So in this problem you only need to find the value of b1.

Step 1 From given data, XYX⋅YX⋅X111132693139 ∑X=7,∑Y=4,∑X⋅Y=10,∑X2=19 Step 2 Regression equation is Y=a+bx where a=∑Y⋅∑X2−∑X⋅∑XYn⋅∑X2−(∑X)2=4⋅19−7⋅103⋅19−72≈0.75 b=n⋅∑XY−∑X⋅∑Yn⋅∑X2−(∑X)2=3⋅10−7⋅43⋅19−(7)2≈0.25 Substitute a and b in regression equation formula y=a+b⋅x y=0.75+0.25⋅x Therefore slope is b1=0.25

Explained: "Find the slope of the regression line for..."

vadulgattp

Answered question

2021-11-26

Find the slope of the regression line for the following data.

\begin{array}{cc} x & y \\ 1 & 1 \\ 3 & 2 \\ 3 & 1 \end{array}

We have written the regression line in the form

y = b_{0} + b_{1} x

. So in this problem you only need to find the value of

b_{1}

Answer & Explanation

Michele Tipton

Beginner2021-11-27Added 11 answers

Step 1
From given data,

\begin{array}{cc} X & Y & X \cdot Y & X \cdot X \\ 1 & 1 & 1 & 1 \\ 3 & 2 & 6 & 9 \\ 3 & 1 & 3 & 9 \end{array}

\sum X = 7, \sum Y = 4, \sum X \cdot Y = 10, \sum X^{2} = 19

Step 2
Regression equation is

Y = a + b x

where

a = \frac{\sum Y \cdot \sum X^{2} - \sum X \cdot \sum X Y}{n \cdot \sum X^{2} - {(\sum X)}^{2}} = \frac{4 \cdot 19 - 7 \cdot 10}{3 \cdot 19 - 7^{2}} \approx 0.75

b = \frac{n \cdot \sum X Y - \sum X \cdot \sum Y}{n \cdot \sum X^{2} - {(\sum X)}^{2}} = \frac{3 \cdot 10 - 7 \cdot 4}{3 \cdot 19 - {(7)}^{2}} \approx 0.25

Substitute a and b in regression equation formula

y = a + b \cdot x

y = 0.75 + 0.25 \cdot x

Therefore slope is

b 1 = 0.25

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