Get the solution to "Use linear regression to find the equation for..."

hvacwk

Answered question

2021-12-06

\begin{array}{cc} Use linear regression to find the equation for the linear function that best fits this data. Round both numbers to two decimal places. Write your final answer in a form of an equation y = m x + b y = m x + b \\ x 1 2 3 4 5 6 \\ y 77 95 123 134 159 184 \end{array}

Answer & Explanation

enhebrevz

Beginner2021-12-07Added 25 answers

Step 1
The mean of the x values

= M_{x} = \frac{1 + 2 + 3 + 4 + 5 + 6}{6} = 3.5

The mean of the y values

= M_{y} = \frac{77 + 95 + 123 + 134 + 159 + 184}{6} = 128.6667

Then we make a table:

\begin{array}{cc} Y - M_{x} & Y - M_{y} & (X - M_{x})^{2} & (X - M_{x}) (Y - M_{y}) \\ - 2.5 & - 51.6667 & 6.25 & 129.1667 \\ - 1.5 & - 33.6667 & 2.25 & 50.5 \\ - 0.5 & - 5.6667 & 0.25 & 2.8333 \\ 0.5 & 5.3333 & 0.25 & 2.6667 \\ 1.5 & 30.3333 & 2.25 & 45.5 \\ 2.5 & 55.3333 & 6.25 & 138.3333 \\ T o t a l & Sum of squares = S S : 17.5 & Sum of products = S P : 369 \end{array}

Step 2

m = \frac{S P}{S S} = \frac{369}{17.5} = 21.08571 \approx 21.09

b = M_{y} - m M_{x} = 128.6667 - (21.08571 \times 3.5) = 54.866715 \approx 54.87

So,

y = m x + b

gives:

y = 21.09 x + 54.87

Answer:

y = 21.09 x + 54.87

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