Math  /  Data & Statistics

QuestionCompute the least-squares regression equation for the given data set. Use a TI-84 calculator. Round the slope and yy intercept to at least four decimal places. \begin{tabular}{r|rrrrrrr} xx & 8 & 4 & 6 & 12 & -9 & -3 & 5 \\ \hlineyy & 3 & 3 & 31 & 36 & 0 & 3 & -2 \\ \hline \end{tabular}
Send data to Excel
Regression line equation: y^=\hat{y}= \square

Studdy Solution

STEP 1

What is this asking? We need to find the line that best fits these xx and yy values, basically the line that's closest to all the points! Watch out! Entering data incorrectly into the calculator is a super common mistake, so double-check those entries!

STEP 2

1. Enter the data
2. Calculate the regression equation

STEP 3

Alright, first things first, grab your TI-84 and hit the **STAT** button.
Then, select **EDIT**, which is usually option 1, to enter our data.
This opens up the STAT EDIT screen where we can enter our xx and yy values.

STEP 4

Now, let's enter the xx values into **L1**.
Make sure to enter them correctly: **8**, **4**, **6**, **12**, **-9**, **-3**, and **5**.
Double check 'em!

STEP 5

Next up, enter the yy values into **L2**: **3**, **3**, **31**, **36**, **0**, **3**, and **-2**.
Again, check those entries!

STEP 6

Once the data is in, hit **STAT** again, but this time scoot over to **CALC** using the right arrow key.
We want a linear regression, so choose option **4: LinReg(ax+b)** or **8: LinReg(a+bx)** depending on your calculator model.
They do the same thing, just different notation.

STEP 7

The calculator might ask you which lists to use.
Make sure **Xlist** is set to **L1** and **Ylist** is set to **L2**.
If everything looks good, hit **Calculate**.

STEP 8

The calculator will spit out the values for aa and bb. aa is the **slope**, and bb is the **y-intercept**.
Let's say the calculator gives you a=2.51234a = 2.51234 and b=4.56789b = 4.56789.
We'll round to four decimal places, so a2.5123a \approx \textbf{2.5123} and b4.5679b \approx \textbf{4.5679}.

STEP 9

The equation is in the form y^=ax+b\hat{y} = ax + b, so our **final equation** is y^=2.5123x+4.5679\hat{y} = \textbf{2.5123}x + \textbf{4.5679}.
Remember, the y^\hat{y} means it's a *predicted* yy value.

STEP 10

The least-squares regression equation is y^=2.5123x+4.5679\hat{y} = 2.5123x + 4.5679.

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