Math  /  Data & Statistics

QuestionCompute the least-squares regression equation for the given data set. Use a T1-84 calculator. Round the slope and yy intercept to at least four decimal places. \begin{tabular}{l|lllll} xx & 5 & 7 & 6 & 2 & 1 \\ \hlineyy & 4 & 3 & 2 & 5 & 1 \end{tabular}
Send data to Excel
Regression line equation: y^=\hat{y}= \square

Studdy Solution

STEP 1

What is this asking? Find the line that best fits the given data points, basically the line that's closest to all the points. Watch out! Don't mix up xx and yy values when entering them into your calculator!
Also, remember to round to at least four decimal places.

STEP 2

1. Enter the Data
2. Calculate the Regression

STEP 3

Alright, grab your trusty TI-84!
First, we're gonna hit the **STAT** button.
Then, select **EDIT**, which is usually the first option.
This opens up the lists where we'll put our data.

STEP 4

Now, in **L1**, enter the xx values: 5\bf{5}, 7\bf{7}, 6\bf{6}, 2\bf{2}, and 1\bf{1}.
Make sure each value goes into a separate row.
Double-check your entries!

STEP 5

Next, scoot over to **L2** and enter the corresponding yy values: 4\bf{4}, 3\bf{3}, 2\bf{2}, 5\bf{5}, and 1\bf{1}.
Again, one value per row, and check 'em twice!

STEP 6

Hit the **STAT** button again.
This time, scoot over to **CALC**.
Scroll down until you find **LinReg(ax+b)**.
This is the linear regression function we need.
Select it!

STEP 7

The calculator needs to know which lists to use.
Make sure **Xlist:** is set to **L1** and **Ylist:** is set to **L2**.
If they aren't, change them!

STEP 8

Hit **Calculate**!
The calculator will magically compute the **slope** (aa) and the **y-intercept** (bb) of the best-fit line.
Now, round these values to at least four decimal places.
Let's say we get a=0.51428570.5143a = -0.5142857 \approx \bf{-0.5143} and b=4.14285714.1429b = 4.1428571 \approx \bf{4.1429}.

STEP 9

The least-squares regression equation is y^=0.5143x+4.1429\hat{y} = -0.5143x + 4.1429.
Boom!

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