Use technology to perform a linear regression to determine the equation for the line of best fit for this data. Estimate the value of y when x=25.

Question

x: 20, 22, 24, 26, 28

y: 9, 12, 16, 20, 23

Please explain the steps clearly. I don't know how to use a linear regression/graphing calculator. I also don't have one.

Answer 1

Hi Alia,

I'll answer this assuming that you will be using desmos. You can find it by googling desmos and then selecting the Graphing Calculator.

In the upper left hand corner, select the plus symbol "+" and then click "table" on the down-select menu. This will give you a table with x₁ and y₁ at the top. Type in the numbers like this:

x₁ y₁

20 9

22 12

24 16

26 20

28 23

Once those are entered, click below the table in the blank space to get a new row on that left side. In this row, you will type in the general equation of a line y = mx + b (since you are doing a LINEAR regression). But you will need to tell desmos that you are using the table of values you just put in for your "y" and "x" so instead of y = mx + b, you type y₁ = mx₁ + b and instead of the equal sign, since you are approximating the best fit line, you put "~". So your equation will look like this:

"y₁ ~ mx₁ + b"

To get the "1" after the y, type the "y" and then the underscore key, then "1". To get "out" of that subscript notation, press your cursor right button. Then type the "~" (squiggle) symbol, then "m" then "x₁" using the underscore button again, then cursor right again, the "+b". That should give you:

"y₁ ~ mx₁ + b"

Once you type this in, information will populate below your equation. It will look like this:

STATISTCS RESIDUALS

r² = 0.9969 e₁ plot

r = 0.9985

PARAMETERS

m = 1.8

b = -27.2

The r² and the r tell you how good your line fit is. The closer to 1 you get, the better. Yiou are very close to 1 so this is a very good fit.

The m = 1.8 and b = -27.2 tell you the equation of your line. So it is y = 1.8x - 27.2 (the answer to your first question).

To find the answer to the second question, take the equation and plug in x = 25 so:

y = 1.8x - 27.2

y = 1.8(25) - 27.2

y = 45 - 27.2

y = 17.8

Answer 2

desmos.com/calculator/shv9gyh5qw