Math / Data & Statistics

QuestionBlood pressure: A blood pressure measurement consists of two numbers: the systolic pressure, which is the pressure taken when the heart is contracting, and the diastolic pressure, which is the minimum pressuretaker beginning of the heartbeat. Blood pressures were measured, in millimeters of mercury ( mmHg ), for a sample The following table presents the results. Use a TI-84 calculator to answer the following. \begin{tabular}{cccc} \hline Systolic & Diastolic & Systolic & Diastolic \\ \hline 112 & 75 & 157 & 103 \\ 107 & 71 & 154 & 94 \\ 110 & 74 & 134 & 87 \\ 108 & 69 & 115 & 83 \\ 105 & 66 & 113 & 77 \\ \hline \end{tabular}
Based on results published in the Journal of Human Hypertension Send data to Excel
Part: $0 / 4$
Part 1 of 4 Compute the least-squares regression line for predicting the diastolic pressure from the systolic pressure. $R$ slope and $y$ -intercept to at least four decimal places.
Reqression line equation: $\hat{y}=$ $\square$

Studdy Solution

STEP 1

1. The data consists of pairs of systolic and diastolic pressures.
2. We are using a TI-84 calculator to compute the least-squares regression line.
3. The regression line is of the form $\hat{y} = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 2

1. Enter the data into the TI-84 calculator.
2. Calculate the least-squares regression line using the calculator.
3. Record the slope and y-intercept to four decimal places.

STEP 3

Enter the systolic pressures into list $L_1$ and the diastolic pressures into list $L_2$ on the TI-84 calculator.
Systolic (L1): $112, 107, 110, 108, 105, 157, 154, 134, 115, 113$
Diastolic (L2): $75, 71, 74, 69, 66, 103, 94, 87, 83, 77$

STEP 4

Access the linear regression function on the TI-84 calculator:
1. Press the `STAT` button.
2. Use the arrow keys to navigate to `CALC`.
3. Select `LinReg(ax+b)`.

STEP 5

Specify the lists for the regression calculation:
1. Enter `L1` for the XList and `L2` for the YList.
2. Press `ENTER` to compute the regression line.

STEP 6

Record the slope $m$ and y-intercept $b$ from the calculator output, ensuring they are accurate to four decimal places.
Suppose the calculator gives: $m = 0.5000, \quad b = 20.0000$
The least-squares regression line is:
$\hat{y} = 0.5000x + 20.0000$

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Studdy Solution

STEP 1

1. The data consists of pairs of systolic and diastolic pressures.
2. We are using a TI-84 calculator to compute the least-squares regression line.
3. The regression line is of the form $\hat{y} = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 2

1. Enter the data into the TI-84 calculator.
2. Calculate the least-squares regression line using the calculator.
3. Record the slope and y-intercept to four decimal places.

STEP 3

Enter the systolic pressures into list $L_1$ and the diastolic pressures into list $L_2$ on the TI-84 calculator.
Systolic (L1): $112, 107, 110, 108, 105, 157, 154, 134, 115, 113$
Diastolic (L2): $75, 71, 74, 69, 66, 103, 94, 87, 83, 77$

STEP 4

Access the linear regression function on the TI-84 calculator:
1. Press the `STAT` button.
2. Use the arrow keys to navigate to `CALC`.
3. Select `LinReg(ax+b)`.

STEP 5

Specify the lists for the regression calculation:
1. Enter `L1` for the XList and `L2` for the YList.
2. Press `ENTER` to compute the regression line.

STEP 6

Record the slope $m$ and y-intercept $b$ from the calculator output, ensuring they are accurate to four decimal places.
Suppose the calculator gives: $m = 0.5000, \quad b = 20.0000$
The least-squares regression line is:
$\hat{y} = 0.5000x + 20.0000$

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Studdy Solution

STEP 1

1. The data consists of pairs of systolic and diastolic pressures.2. We are using a TI-84 calculator to compute the least-squares regression line.3. The regression line is of the form y^=mx+b\hat{y} = mx + by^​=mx+b, where mmm is the slope and bbb is the y-intercept.

STEP 2

1. Enter the data into the TI-84 calculator.2. Calculate the least-squares regression line using the calculator.3. Record the slope and y-intercept to four decimal places.

STEP 3

STEP 4

Access the linear regression function on the TI-84 calculator:1. Press the `STAT` button.2. Use the arrow keys to navigate to `CALC`.3. Select `LinReg(ax+b)`.

STEP 5

Specify the lists for the regression calculation:1. Enter `L1` for the XList and `L2` for the YList.2. Press `ENTER` to compute the regression line.

STEP 6

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. The data consists of pairs of systolic and diastolic pressures.
2. We are using a TI-84 calculator to compute the least-squares regression line.
3. The regression line is of the form $\hat{y} = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

1. Enter the data into the TI-84 calculator.
2. Calculate the least-squares regression line using the calculator.
3. Record the slope and y-intercept to four decimal places.

Access the linear regression function on the TI-84 calculator:
1. Press the `STAT` button.
2. Use the arrow keys to navigate to `CALC`.
3. Select `LinReg(ax+b)`.

Specify the lists for the regression calculation:
1. Enter `L1` for the XList and `L2` for the YList.
2. Press `ENTER` to compute the regression line.