Question

1.   Regression analysis is to be conducted with data from vegetarians to see whether the number of grams of protein each ate per day was related to diastolic blood pressure.   The resulting regression formula will be used by medical personnel to predict blood pressure in a weight loss clinic in downtown Pittsburgh.

Subject	Grams of protein	Diastolic BP
1	4	73
2	6.5	79
3	5	83
4	5.5	82
5	8	84
6	10	92
7	9	88
8	8.2	86
9	10.5	95

a. Which variable is the response/dependent variable?

b. Which is the explanatory/independent variable?

c. Develop a scatter diagram for these data. How would you interpret the scatterplot?

Run a regression analysis of the data on Excel. Use your output to answer the following:

d. What is the value of the correlation coefficient between grams of protein and blood pressure? What does is say about the strength of the relationship?

e. What is the value of the coefficient of determination? How would you interpret it?

f. Write the hypotheses for the test of the slope.

g. What is the p-value for the test of the slope? How would you interpret it?

h. What is the least squares regression formula?

i. Use your formula to predict the diastolic blood pressure for someone who consumes 7 grams of protein per day.

j. Use your formula to predict the diastolic blood pressure for someone who consumes 13 grams of protein per day.

2. A researcher wants to determine the relationship between the typing speed of administrative assistants at a major university is related to the time that it takes for the admin assistant to learn to use a new software program and may be used to predict learning time. Data are gathered from 12 departments at the university.

Dept	Typing speed (words per minute)	Learning time (hours)
A	48	7
B	74	4
C	52	8
D	79	3.5
E	83	2
F	56	6
G	85	2.3
H	63	5
I	88	2.1
J	74	4.5
K	90	1.9
L	92	1.5

a. Which variable is the response/dependent variable?

b. Which is the explanatory/independent variable?

c. Develop a scatter diagram for these data. How would you interpret the scatterplot?

Run a regression analysis of the data on Excel. Use your output to answer the following:

d. What is the value of the correlation coefficient between typing speed and learning time? What does is say about the strength of the relationship?

e. What is the value of the coefficient of determination? How would you interpret it?

f. Write the hypotheses for the test of the slope.

g. What is the p-value for the test of the slope? How would you interpret it?

h. What is the least squares regression formula?

i. Use your formula to predict the learning time for an assistant who types 80 words per minute.

j. Use your formula to predict the learning time for an assistant who types 60 words per minute.

Answer 1

Q1 )

a) Dependent Variable : diastolic blood pressure

b) Independent Variable : Consumption of protein (grams of protein)

c) Scatter Diagram

There is positive strong correlation between grams of protein and diastolic bp.

d) The value of Correlation Coefficient is r = 0.9160

There is strong positive relationship between grams of protein and diastolic bp.

e) Coefficient of determination R² = 0.8390

83.9% of the varaition in diastolic bp is explained by the variation in grams of protein.

f) Null Hypothesis

Alternative Hypothesis

g) The p-value for the test of the slope is 0.000521

h) The least square regression is

i) When X = 7

j) When X = 13