Key to "Find the linear regression line for a scatterplot..."

Kye

Answered question

2021-01-31

Find the linear regression line for a scatterplot formed by the points

(10, 261), (21, 252), (42, 209), (33, 163),

and

(52, 98) .

Round to the nearest tenth.

Answer & Explanation

Arnold Odonnell

Skilled2021-02-01Added 109 answers

Step 1
The first value in each point represents the x-value, while the second value in each point represents the y-value.
$\begin{array}{cc} x & y \\ 10 & 261 \\ 21 & 252 \\ 42 & 209 \\ 33 & 163 \\ 52 & 98 \end{array}$
Press on the Stat-button and then on press on ENTER (by which we will select 1:Edit...).
Enter the x-value in the list L1 and enter y-values in the list L2.
Next press on STAT, press $△ r i g h t$ (to select the CALC-tab), press $△ d o w n$ three times until 4:LinReg $(a x + b)$ is selected and then press on ENTER.
Next press 2nd and STAT (to open the LIST-menu) and press ENTER to select 1:L1.
Next press on "," (comma). Then press 2nd and STAT (to open the LIST-menu), press $△ d o w n$ once and press ENTER to select 2:L2.
$L \in R e g (a x + b) L_{1}, L_{2}$
Finally, press enter again.
Result graphing calculator:
$y = a x + b$
$a = - 3.5358$
$b = 308.3322$
$r^{2} = 0.7583$
$r = - 0.8708$
Step 2
Thus $a \approx - 3.54$ and $b \approx 308.33$ in $y = a x + b$
$y = a x + b = - 3.54 x + 308.33$

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