Give the following data, which is the equation of the regression line? X034512Y826912 a. y=4.88+0.625x b. y=4.98+0.425x c. y=4.98+0.725 d. y=4.88+0.525

Step 1 Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question specifying the one you’d like answered. Solution: Given: X034512Y826912 Equation of regression line is, Y=a+bX where, a=(∑y)(∑x2)−∑x(∑xy)n(∑x2)−(∑x)2 b=n(∑xy)−(∑x)(∑y)n(∑x2)−(∑x)2 Step 2 Table for calculation: XYXYX2080032694624165945251212144144∑=24∑=37∑=219∑=194 ∴a=37×194−24×2195×194−242 =4.88 and b=5×219−24×375×194−242 =0.525 Therefore regression equation is, Y=4.88+0.525X Answer : Equation of regression line is Y=4.88+0.525X.

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Teddy Dillard

Answered question

2021-12-11

Give the following data, which is the equation of the regression line?

\begin{array}{cc} X & 0 & 3 & 4 & 5 & 12 \\ Y & 8 & 2 & 6 & 9 & 12 \end{array}

y = 4.88 + 0.625 x

y = 4.98 + 0.425 x

y = 4.98 + 0.725

y = 4.88 + 0.525

Answer & Explanation

Debbie Moore

Beginner2021-12-12Added 43 answers

Step 1
Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question specifying the one you’d like answered.
Solution:
Given:

\begin{array}{cc} X & 0 & 3 & 4 & 5 & 12 \\ Y & 8 & 2 & 6 & 9 & 12 \end{array}

Equation of regression line is,

Y = a + b X

where,

a = \frac{(\sum y) (\sum x^{2}) - \sum x (\sum x y)}{n (\sum x^{2}) - {(\sum x)}^{2}}

b = \frac{n (\sum x y) - (\sum x) (\sum y)}{n (\sum x^{2}) - {(\sum x)}^{2}}

Step 2
Table for calculation:

\begin{array}{cc} X & Y & X Y & X^{2} \\ 0 & 8 & 0 & 0 \\ 3 & 2 & 6 & 9 \\ 4 & 6 & 24 & 16 \\ 5 & 9 & 45 & 25 \\ 12 & 12 & 144 & 144 \\ \sum = 24 & \sum = 37 & \sum = 219 & \sum = 194 \end{array}

∴ a = \frac{37 \times 194 - 24 \times 219}{5 \times 194 - 24^{2}}

= 4.88

and

b = \frac{5 \times 219 - 24 \times 37}{5 \times 194 - 24^{2}}

= 0.525

Therefore regression equation is,

Y = 4.88 + 0.525 X

Answer : Equation of regression line is

Y = 4.88 + 0.525 X

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