Question

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.

Data:
Age, x,  HDL Cholesterol, y
36   56
41   55
47   32
30   56
54   37
51   40
59   40
61   39
25   47
36   43
65   61
29   55
53   38
25   47
54   38
50   53
41   27

​(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 linear.

B. The relation appears to be nonlinear.

C. There does not appear to be a relation.

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

ModifyingAbove y with caret equals y=?x+? (Round to three decimal places as​ needed.)

(c) Are there any outliers or influential​ observations?

No

Yes

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

The​ P-value is ​(Round to three decimal places as​ needed.)

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=
Upper Bound	equals=

​(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. Yes, because the null hypothesis was not rejected.

C. ​No, because the null hypothesis was not rejected.

D. ​No, because the null hypothesis was rejected.

A good estimate for the HDL cholesterol of this patient is ? (Round to two decimal places as needed)

Answer 1

a)

B. The relation appears to be nonlinear

b)

Coefficientsa
Model	Unstandardized Coefficients	Standardized Coefficients	t	Sig.
B	Std. Error	Beta
1	(Constant)	53.585	8.785		6.100	0.000
Age	-0.194	0.190	-0.255	-1.021	0.323
a. Dependent Variable: HDL_Cholestrol

HDL_Cholestrol = 53.585 - 0.194Age

c)

Yes

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

Coefficientsa
Model	Unstandardized Coefficients	Standardized Coefficients	t	Sig.	95.0% Confidence Interval for B
B	Std. Error	Beta	Lower Bound	Upper Bound
1	(Constant)	53.585	8.785		6.100	0.000	34.860	72.310
Age	-0.194	0.190	-0.255	-1.021	0.323	-0.599	0.211
a. Dependent Variable: HDL_Cholestrol

Lower Bound	equals=	-0.599
Upper Bound	equals=	0.211

​(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?

A. Yes, because the null hypothesis was rejected

A good estimate for the HDL cholesterol of this patient is 45.437