A doctor wanted to determine whether there is a relation between a male's age and his HDL (so-called good) cholesterol. The doctor randomly selected 17 of his patients and determined their HDL cholesterol. The data obtained by the doctor is the in the data table below. Complete parts (a) through (f) below. Age vs. HDL Cholesterol data Age, x HDL Cholesterol, y Age, x HDL Cholesterol, y 3838 5555 4040 4343 4141 5454 6767 6464 4747 3535 2929 5353 3232 5656 5050 3737 5454 3434 2626 4444 5252 3939 5151 3636 6060 4444 4747 5353 6161 3838 4040 2828 2626 4949 PrintDone view the data obtained by the doctor. obtained by the doctor is the in the data table below. Complete parts (a) through (f) below. LOADING... Click the icon to view the data obtained by the doctor. (a) Draw a scatter diagram of the data, treating age as the explanatory variable. What type of relation, if any, appears to exist between age and HDL cholesterol? A. The relation appears to be nonlinear. B. There does not appear to be a relation. Your answer is correct. C. The relation appears to be linear. (b) Determine the least-squares regression equation from the sample data. ModifyingAbove y with caret equalsy=negative (Round to three decimal places as needed.) (c) Are there any outliers or influential observations? No Your answer is correct. Yes (d) Assuming the residuals are normally distributed, test whether a linear relation exists between age and HDL cholesterol levels at the alphaαequals level of significance. What are the null and alternative hypotheses? A. Upper H 0H0: beta 1β1equals=0; Upper H 1H1: beta 1β1greater than>0 B. Upper H 0H0: beta 1β1equals=0; Upper H 1H1: beta 1β1less than<0 C. Upper H 0H0: beta 1β1equals=0; Upper H 1H1: beta 1β1not equals≠0 Your answer is correct. Use technology to compute the P-value. Use the Tech Help button for further assistance. The P-value is 0.5700.570. (Round to three decimal places as needed.) What conclusion can be drawn at alphaαequals= level of significance? A. RejectReject the null hypothesis because the P-value is greatergreater than alphaαequals B. RejectReject the null hypothesis because the P-value is lessless than alphaαequals= C. Do not rejectDo not reject the null hypothesis because the P-value is lessless than alphaαequals= D. Do not rejectDo not reject the null hypothesis because the P-value is greatergreater than alphaαequals=0.010.01. Your answer is correct. (e) Assuming the residuals are normally distributed, construct a 95% confidence interval about the slope of the true least-squares regression line. Lower Bound equals= negative 0.554−0.554 Upper Bound equals= 0.3170.317 (Round to three decimal places as needed.) (f) For a 42-year-old male patient who visits the doctor's office, would using the least-squares regression line obtained in part (b) to predict the HDL cholesterol of this patient be recommended? If the null hypothesis was rejected, that means that this least-squares regression line can accurately predict the HDL cholesterol of a patient. If the null hypothesis was not rejected, that means the least-squares regression line cannot accurately predict the HDL cholesterol of a patient. Should this least-squares regression line be used to predict the patient's HDL cholesterol? Choose the correct answer below. A. Yes, because the null hypothesis was rejected. B. No, because the null hypothesis was rejected. C. Yes, because the null hypothesis was not rejected. D. No, because the null hypothesis was not rejected. Your answer is correct. A good estimate for the HDL cholesterol of this patient is (Round to two decimal places as needed.)

A doctor wanted to determine whether there is a relation between a male's age and his HDL (so-called good) cholesterol. The doctor randomly selected 17 of his patients and determined their HDL cholesterol. The data obtained by the doctor is the in the data table below. Complete parts (a) through (f) below. Age vs. HDL Cholesterol data Age, x HDL Cholesterol, y Age, x HDL Cholesterol, y 3838 5555 4040 4343 4141 5454 6767 6464 4747 3535 2929 5353 3232 5656 5050 3737 5454 3434 2626 4444 5252 3939 5151 3636 6060 4444 4747 5353 6161 3838 4040 2828 2626 4949 PrintDone view the data obtained by the doctor. obtained by the doctor is the in the data table below. Complete parts (a) through (f) below. LOADING... Click the icon to view the data obtained by the doctor. (a) Draw a scatter diagram of the data, treating age as the explanatory variable. What type of relation, if any, appears to exist between age and HDL cholesterol? A. The relation appears to be nonlinear. B. There does not appear to be a relation. Your answer is correct. C. The relation appears to be linear. (b) Determine the least-squares regression equation from the sample data. ModifyingAbove y with caret equalsy=negative (Round to three decimal places as needed.) (c) Are there any outliers or influential observations? No Your answer is correct. Yes (d) Assuming the residuals are normally distributed, test whether a linear relation exists between age and HDL cholesterol levels at the alphaαequals level of significance. What are the null and alternative hypotheses? A. Upper H 0H0: beta 1β1equals=0; Upper H 1H1: beta 1β1greater than>0 B. Upper H 0H0: beta 1β1equals=0; Upper H 1H1: beta 1β1less than<0 C. Upper H 0H0: beta 1β1equals=0; Upper H 1H1: beta 1β1not equals≠0 Your answer is correct. Use technology to compute the P-value. Use the Tech Help button for further assistance. The P-value is 0.5700.570. (Round to three decimal places as needed.) What conclusion can be drawn at alphaαequals= level of significance? A. RejectReject the null hypothesis because the P-value is greatergreater than alphaαequals B. RejectReject the null hypothesis because the P-value is lessless than alphaαequals= C. Do not rejectDo not reject the null hypothesis because the P-value is lessless than alphaαequals= D. Do not rejectDo not reject the null hypothesis because the P-value is greatergreater than alphaαequals=0.010.01. Your answer is correct. (e) Assuming the residuals are normally distributed, construct a 95% confidence interval about the slope of the true least-squares regression line. Lower Bound equals= negative 0.554−0.554 Upper Bound equals= 0.3170.317 (Round to three decimal places as needed.) (f) For a 42-year-old male patient who visits the doctor's office, would using the least-squares regression line obtained in part (b) to predict the HDL cholesterol of this patient be recommended? If the null hypothesis was rejected, that means that this least-squares regression line can accurately predict the HDL cholesterol of a patient. If the null hypothesis was not rejected, that means the least-squares regression line cannot accurately predict the HDL cholesterol of a patient. Should this least-squares regression line be used to predict the patient's HDL cholesterol? Choose the correct answer below. A. Yes, because the null hypothesis was rejected. B. No, because the null hypothesis was rejected. C. Yes, because the null hypothesis was not rejected. D. No, because the null hypothesis was not rejected. Your answer is correct. A good estimate for the HDL cholesterol of this patient is (Round to two decimal places as needed.)

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Description: A doctor wanted to determine whether there is a relation between a male's age and his HDL (so-called good) cholesterol. The doctor randomly selected 17 of his patients and determined their HDL cholesterol. The data obtained by the doctor is the in

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Age vs. HDL Cholesterol data

Age, x	HDL Cholesterol, y	Age, x	HDL Cholesterol, y
3838	5555	4040	4343
4141	5454	6767	6464
4747	3535	2929	5353
3232	5656	5050	3737
5454	3434	2626	4444
5252	3939	5151	3636
6060	4444	4747	5353
6161	3838	4040	2828
2626	4949

PrintDone

view the data obtained by the doctor.

obtained by the doctor is the in the data table below. Complete parts (a) through (f) below.

Click the icon to view the data obtained by the doctor.

(a) Draw a scatter diagram of the data, treating age as the explanatory variable. What type of relation, if any, appears to exist between age and HDL cholesterol?

The relation appears to be nonlinear.

There does not appear to be a relation.

Your answer is correct.

The relation appears to be linear.

(b) Determine the least-squares regression equation from the sample data.

ModifyingAbove y with caret equalsy=negative

(Round to three decimal places as needed.)

Your answer is correct.

Yes

(d) Assuming the residuals are normally distributed, test whether a linear relation exists between age and HDL cholesterol levels at the

alphaαequals

level of significance.

What are the null and alternative hypotheses?

Upper H 0H0:

beta 1β1equals=0;

Upper H 1H1:

beta 1β1greater than>0

Upper H 0H0:

beta 1β1equals=0;

Upper H 1H1:

beta 1β1less than<0

Upper H 0H0:

beta 1β1equals=0;

Upper H 1H1:

beta 1β1not equals≠0

Your answer is correct.

Use technology to compute the P-value. Use the Tech Help button for further assistance.

The P-value is

0.5700.570.

(Round to three decimal places as needed.)

What conclusion can be drawn at

alphaαequals=

level of significance?

RejectReject

the null hypothesis because the P-value is

greatergreater

than

alphaαequals

RejectReject

the null hypothesis because the P-value is

lessless

than

alphaαequals=

Do not rejectDo not reject

the null hypothesis because the P-value is

lessless

than

alphaαequals=

Do not rejectDo not reject

the null hypothesis because the P-value is

greatergreater

than

alphaαequals=0.010.01.

Your answer is correct.

(e) Assuming the residuals are normally distributed, construct a 95% confidence interval about the slope of the true least-squares regression line.

Lower Bound	equals=	negative 0.554−0.554
Upper Bound	equals=	0.3170.317

(Round to three decimal places as needed.)

(f) For a 42-year-old male patient who visits the doctor's office, would using the least-squares regression line obtained in part (b) to predict the HDL cholesterol of this patient be recommended?

If the null hypothesis was rejected, that means that this least-squares regression line can accurately predict the HDL cholesterol of a patient. If the null hypothesis was not rejected, that means the least-squares regression line cannot accurately predict the HDL cholesterol of a patient.

Should this least-squares regression line be used to predict the patient's HDL cholesterol? Choose the correct answer below.

Yes, because the null hypothesis was rejected.

No, because the null hypothesis was rejected.

Yes, because the null hypothesis was not rejected.

No, because the null hypothesis was not rejected.

Your answer is correct.

A good estimate for the HDL cholesterol of this patient is

(Round to two decimal places as needed.)

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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