Math  /  Data & Statistics

QuestionBlood pressure: A blood pressure measurement consists of two numbers: the systolic pressure, which is the maximum pressure taken when the heart is contracting, and the diastolic pressure, which is the minimum pressure taken at the beginning of the heartbeat. Blood pressures were measured, in millimeters of mercury ( mmHg ), for a sample of 10 adults. The following table presents the results. Use a T1-84 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: 0/40 / 4
Part 1 of 4
Compute the least-squares regression line for predicting the diastolic pressure from the systolic pressure. Round the slope and yy-intercept to at least four decimal places.
Regression line equation: y^=\hat{y}= \square

Studdy Solution

STEP 1

What is this asking? We need to find the line that *best* predicts diastolic blood pressure using systolic blood pressure measurements, and give its equation in the form y^=mx+b\hat{y} = mx + b. Watch out! Don't mix up systolic and diastolic, and remember we're predicting diastolic *from* systolic.
Also, keep track of those decimals!

STEP 2

1. Enter the data
2. Calculate the regression line

STEP 3

Alright, future doctors, let's **enter our data** into our trusty TI-84!
Hit **STAT**, then **EDIT**.
Enter the systolic pressures (those first numbers) into **L1** and the diastolic pressures (the second numbers) into **L2**.
Double-check your entries, accuracy is key!

STEP 4

Now for the magic!
Press **STAT**, scroll over to **CALC**, and choose **LinReg(ax+b)**.
Make sure **Xlist** is set to **L1** and **Ylist** is set to **L2**.
Go down to **Calculate** and hit **ENTER**.

STEP 5

Boom! Your calculator should display the **slope** (aa) and **y-intercept** (bb) of the least-squares regression line.
Let's round these values to four decimal places as requested.
Suppose your calculator shows a0.71568a \approx 0.71568 and b6.8931b \approx -6.8931.
Rounding to four decimal places gives us a0.7157a \approx \mathbf{0.7157} and b6.8931b \approx \mathbf{-6.8931}.

STEP 6

The equation of our regression line is y^=ax+b\hat{y} = ax + b.
Substituting our rounded values, we get y^=0.7157x6.8931\hat{y} = \mathbf{0.7157}x - \mathbf{6.8931}.
Remember, xx represents the systolic pressure, and y^\hat{y} is the *predicted* diastolic pressure.

STEP 7

The least-squares regression line equation for predicting diastolic pressure (y^\hat{y}) from systolic pressure (xx) is y^=0.7157x6.8931\hat{y} = \mathbf{0.7157}x - \mathbf{6.8931}.

Was this helpful?

Studdy solves anything!

banner

Start learning now

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

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord