A recent 10-year study conducted by a research team at the Great Falls Medical School was conducted to assess how age, systolic blood pressure, and smoking relate to the risk of strokes. Assume that the following data are from a portion of this study. Risk is interpreted as the probability (times 100) that the patient will have a stroke over the next 10-year period. For the smoking variable, define a dummy variable with 1 indicating a smoker and 0 indicating a nonsmoker.

Risk
Age Systolic
Blood
Pressure
Smoker

11 58 152 Yes

24 65 163 No

13 58 155 No

56 86 177 Yes

27 59 196 Yes

51 76 189 Yes

18 56 155 Yes

31 78 120 No

37 80 135 Yes

15 78 98 No

22 71 152 No

36 70 173 Yes

15 67 135 Yes

48 77 209 Yes

15 60 199 No

36 82 119 Yes

8 66 166 No

34 80 125 Yes

3 62 117 No

38 59 209 Yes

(a) Develop an estimated multiple regression equation that relates risk of a stroke to the person's age, systolic blood pressure, and whether the person is a smoker.

Let x₁ represent the person's age.

Let x₂ represent the person's systolic blood pressure.

Let x₃ represent whether the person is a smoker.

If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)

= + x₁ + x₂ + x₃

(b) Is smoking a significant factor in the risk of a stroke? Explain. Use a 0.05 level of significance.

We reject the hypothesis that β₃ = 0, implying there sufficient evidence to conclude that smoking is a significant factor in the risk of a stroke.

(c) What is the probability of a stroke over the next 10 years for Art Speen, a 65-year-old smoker who has a systolic blood pressure of 165?

If required, round your answer to two decimal places. Do not round intermediate calculations.

What action might the physician recommend for this patient?

The input in the box below will not be graded, but may be reviewed and considered by your instructor.

(d) An insurance company will only sell its Select policy to people for whom the probability of a stroke in the next ten years is less than .01. If a smoker with a systolic blood pressure of 230 applies for a Select policy, under what condition will the company sell him the policy if it adheres to this standard?

(i) The person must be 29 years old or younger.

(ii) The person must be at least 29 years old.

(iii) No smoker can qualify for a Select policy.

(iv) With this blood pressure measure, this person cannot qualify for a Select policy.

(e) What other factors could be included in the model as independent variables? Choose the correct answer below.

(i) Family History of Stroke

(ii) Weight/obesity

(iii) Gender

(iv) All of the above

Question

A recent 10-year study conducted by a research team at the Great Falls Medical School was conducted to assess how age, systolic blood pressure, and smoking relate to the risk of strokes. Assume that the following data are from a portion of this study. Risk is interpreted as the probability (times 100) that the patient will have a stroke over the next 10-year period. For the smoking variable, define a dummy variable with 1 indicating a smoker and 0 indicating a nonsmoker.

Risk	Age	Systolic Blood Pressure	Smoker
11	58	152	Yes
24	65	163	No
13	58	155	No
56	86	177	Yes
27	59	196	Yes
51	76	189	Yes
18	56	155	Yes
31	78	120	No
37	80	135	Yes
15	78	98	No
22	71	152	No
36	70	173	Yes
15	67	135	Yes
48	77	209	Yes
15	60	199	No
36	82	119	Yes
8	66	166	No
34	80	125	Yes
3	62	117	No
38	59	209	Yes

(a)

Develop an estimated multiple regression equation that relates risk of a stroke to the person's age, systolic blood pressure, and whether the person is a smoker.

Let x₁ represent the person's age.

Let x₂ represent the person's systolic blood pressure.

Let x₃ represent whether the person is a smoker.

If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)

= + x₁ + x₂ + x₃

(b)

Is smoking a significant factor in the risk of a stroke? Explain. Use a 0.05 level of significance.

We reject the hypothesis that β₃ = 0, implying there sufficient evidence to conclude that smoking is a significant factor in the risk of a stroke.

(c)

What is the probability of a stroke over the next 10 years for Art Speen, a 65-year-old smoker who has a systolic blood pressure of 165?

If required, round your answer to two decimal places. Do not round intermediate calculations.

What action might the physician recommend for this patient?

The input in the box below will not be graded, but may be reviewed and considered by your instructor.

(d)

An insurance company will only sell its Select policy to people for whom the probability of a stroke in the next ten years is less than .01. If a smoker with a systolic blood pressure of 230 applies for a Select policy, under what condition will the company sell him the policy if it adheres to this standard?

(i)	The person must be 29 years old or younger.
(ii)	The person must be at least 29 years old.
(iii)	No smoker can qualify for a Select policy.
(iv)	With this blood pressure measure, this person cannot qualify for a Select policy.

(e)

What other factors could be included in the model as independent variables? Choose the correct answer below.

(i)	Family History of Stroke
(ii)	Weight/obesity
(iii)	Gender
(iv)	All of the above

Accepted Answer

"Since you have posted a question with multiple sub-parts, we'll solve the first three sub-parts for…