Smoking: Statistics and Linear Regression Equation.

Problems on Regression and Correlation
Prepared by: Dr. Elias Dabeet

Q1. Dr. Green (a pediatrician) wanted to test if there is a correlation between the number of meals consumed by a child per day (X) and the child weight (Y). Included you will find a table containing the information on 5 of the children. Use the table to answer the following:

Child
Number of meals consumed per day (X) child weight (Y)
X²
Y²
XY
Ahmad
11
8
121
64
88
Ali
16
11
256
121
176
Osama
12
9
144
81
108
Husien
19
13
361
169
247
Total
58
41
882
435
619

a. Determine the simple linear regression equation.
b. Determine the correlation coefficient. Interpret it in words.
c. What is the expected child weight if the number of meals increased by 2 meals per day?

Q2. A hospital supervisor wishes to find the relationship between the number of nurses on a job and the number of patients examined for a shift. Listed below is the result for a sample of 4 days. Let the number of patients ( y ) be the dependent variable.

Nurses ( x )
Patients ( y )

9
12

3
14

5
11

8
13

a. Compute , , , , .

b. Determine the coefficient of correlation. Interpret its meaning.

c. Determine the estimated simple linear regression equation.

d. If the number of nurses on a job changes by 3, what is the corresponding change in the number of examined patients.

Q3. A study was conducted on the relation between advertising expenditures and amount of sales for a medical device product, the data are in the following table:

Advertising Expenditures ( $1000 ) x
Amount of Sales ( 1000 units ) y

2
2

4
3

5
2

7
6

8
4

a. Determine the estimated linear regression equation.

b. Determine the coefficient of correlation and the coefficient of determination. Interpret their meanings.

c. Describe the relation between X & Y ( Direct, Inverse).Explain.

c. If the advertising