Math / Data & Statistics

QuestionCompute the least-squares regression equation for the given data set. Use a TI-84 calculator. Round the slope and $y$ intercept to at least four decimal places. \begin{tabular}{l|lllllll} $x$ & 5.8 & 4.2 & 6.3 & 4.4 & 6.6 & 5.9 & 5.0 \\ \hline $y$ & 1.9 & 4.8 & 0.8 & 3.9 & 1.2 & 1.7 & 3.0 \end{tabular}
Send data to Excel
Regression line equation: $\hat{y}=$ $\square$

Studdy Solution

STEP 1

What is this asking? We need to find the line that best fits a bunch of points, the least-squares regression line, and give its equation in the form $\hat{y} = mx + b$ , rounding the slope ( $m$ ) and y-intercept ( $b$ ) to four decimal places! Watch out! Don't mix up $x$ and $y$ values when entering them into your calculator.
Also, make sure your calculator is set to calculate a linear regression!

STEP 2

1. Enter the data
2. Calculate the regression

STEP 3

First, hit the STAT button on your calculator.
This takes us to the statistics menu where all the magic happens!

STEP 4

Select Edit (usually by pressing 1 or ENTER).
Now, carefully enter the $x$ values into L1 and the $y$ values into L2.
Double-check your entries!
Accuracy is key here.

STEP 5

Press STAT again, and then go over to CALC (using the right arrow key).

STEP 6

Scroll down to LinReg(ax+b) and press ENTER.
This tells the calculator we want a linear regression in the form $y = ax + b$ (which is the same as $\hat{y} = mx + b$ , just with different letters for slope and intercept).

STEP 7

Make sure Xlist is set to L1 and Ylist is set to L2.
If they aren't, change them!
Then, go down to Calculate and press ENTER.

STEP 8

The calculator will show you the values for $a$ (the slope, like $m$ ) and $b$ (the y-intercept).
It might also show you $r$ and $r^2$ , which tell you how well the line fits the data, but we don't need those for this problem. Write down the values for $a$ and $b$ , rounding to four decimal places.
For example, if $a = -0.526123$ and $b = 4.187654$ , we'd write down $a \approx -0.5261$ and $b \approx 4.1877$ .

STEP 9

So, if our calculated slope was $a \approx -0.5261$ and our y-intercept was $b \approx 4.1877$ , the least-squares regression equation is $\hat{y} = -0.5261x + 4.1877$ . Replace these example values with the ones you calculated!

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Studdy Solution

STEP 1

STEP 2

1. Enter the data
2. Calculate the regression

STEP 3

First, hit the STAT button on your calculator.
This takes us to the statistics menu where all the magic happens!

STEP 4

Select Edit (usually by pressing 1 or ENTER).
Now, carefully enter the $x$ values into L1 and the $y$ values into L2.
Double-check your entries!
Accuracy is key here.

STEP 5

Press STAT again, and then go over to CALC (using the right arrow key).

STEP 6

Scroll down to LinReg(ax+b) and press ENTER.
This tells the calculator we want a linear regression in the form $y = ax + b$ (which is the same as $\hat{y} = mx + b$ , just with different letters for slope and intercept).

STEP 7

Make sure Xlist is set to L1 and Ylist is set to L2.
If they aren't, change them!
Then, go down to Calculate and press ENTER.

STEP 8

STEP 9

So, if our calculated slope was $a \approx -0.5261$ and our y-intercept was $b \approx 4.1877$ , the least-squares regression equation is $\hat{y} = -0.5261x + 4.1877$ . Replace these example values with the ones you calculated!

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Studdy Solution

STEP 1

STEP 2

1. Enter the data2. Calculate the regression

STEP 3

First, **hit the STAT button** on your calculator.This takes us to the statistics menu where all the magic happens!

STEP 4

Select **Edit** (usually by pressing 1 or ENTER).Now, carefully **enter the xxx values** into L1 and the **yyy values** into L2.Double-check your entries!Accuracy is key here.

STEP 5

**Press STAT again**, and then **go over to CALC** (using the right arrow key).

STEP 6

Scroll down to **LinReg(ax+b)** and press ENTER.This tells the calculator we want a linear regression in the form y=ax+by = ax + by=ax+b (which is the same as y^=mx+b\hat{y} = mx + by^​=mx+b, just with different letters for slope and intercept).

STEP 7

Make sure Xlist is set to L1 and Ylist is set to L2.If they aren't, change them!Then, **go down to Calculate** and press ENTER.

STEP 8

STEP 9

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1. Enter the data
2. Calculate the regression

First, hit the STAT button on your calculator.
This takes us to the statistics menu where all the magic happens!

Select Edit (usually by pressing 1 or ENTER).
Now, carefully enter the $x$ values into L1 and the $y$ values into L2.
Double-check your entries!
Accuracy is key here.

Press STAT again, and then go over to CALC (using the right arrow key).

Scroll down to LinReg(ax+b) and press ENTER.
This tells the calculator we want a linear regression in the form $y = ax + b$ (which is the same as $\hat{y} = mx + b$ , just with different letters for slope and intercept).

Make sure Xlist is set to L1 and Ylist is set to L2.
If they aren't, change them!
Then, go down to Calculate and press ENTER.