This module provides a homework for Linear Regression and Correlation as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.
For each situation below, state the independent variable and the dependent variable.
A study is done to determine if elderly drivers are involved in more motor vehicle fatalities than all other drivers. The number of fatalities per 100,000 drivers is compared to the age of drivers.
A study is done to determine if the weekly grocery bill changes based on the number of family members.
Insurance companies base life insurance premiums partially on the age of the applicant.
Utility bills vary according to power consumption.
A study is done to determine if a higher education reduces the crime rate in a population.
Independent: Age; Dependent: Fatalities
Independent: Power Consumption; Dependent: Utility
In 1990 the number of driver deaths per 100,000 for the different age groups was as follows (Source:
The National Highway Traffic Safety Administration's National Center for Statistics and Analysis ):
Age
Number of Driver Deaths per 100,000
15-24
28
25-39
15
40-69
10
70-79
15
80+
25
For each age group, pick the midpoint of the interval for the x value. (For the 80+ group, use 85.)
Using “ages” as the independent variable and “Number of driver deaths per 100,000” as the dependent variable, make a scatter plot of the data.
Calculate the least squares (best–fit) line. Put the equation in the form of:
Find the correlation coefficient.
Pick two ages and find the estimated fatality rates.
Use the two points in (e) to plot the least squares line on your graph from (b).
Based on the above data, is there a linear relationship between age of a driver and driver fatality rate?
What is the slope of the least squares (best-fit) line? Interpret the slope.
The average number of people in a family that received welfare for various years is given below. (Source:
House Ways and Means Committee, Health and Human Services Department )
Year
Welfare family size
1969
4.0
1973
3.6
1975
3.2
1979
3.0
1983
3.0
1988
3.0
1991
2.9
Using “year” as the independent variable and “welfare family size” as the dependent variable, make a scatter plot of the data.
Calculate the least squares line. Put the equation in the form of:
Find the correlation coefficient.
Pick two years between 1969 and 1991 and find the estimated welfare family sizes.
Use the two points in (d) to plot the least squares line on your graph from (b).
Based on the above data, is there a linear relationship between the year and the average number of people in a welfare family?
Using the least squares line, estimate the welfare family sizes for 1960 and 1995. Does the least squares line give an accurate estimate for those years? Explain why or why not.
Are there any outliers in the above data?
What is the estimated average welfare family size for 1986? Does the least squares line give an accurate estimate for that year? Explain why or why not.
What is the slope of the least squares (best-fit) line? Interpret the slope.
-0.8533
No
No.
2.97, Yes
slope = -0.0432. As the year increases by one, the welfare family size decreases by 0.0432 people.
Step 1: Find the mean. To find the mean, add up all the scores, then divide them by the number of scores. ...
Step 2: Find each score's deviation from the mean. ...
Step 3: Square each deviation from the mean. ...
Step 4: Find the sum of squares. ...
Step 5: Divide the sum of squares by n – 1 or N.
The sample of 16 students is taken. The average age in the sample was 22 years with astandard deviation of 6 years. Construct a 95% confidence interval for the age of the population.
Bhartdarshan' is an internet-based travel agency wherein customer can see videos of the cities they plant to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400
a. what is the probability of getting more than 12,000 hits?
b. what is the probability of getting fewer than 9,000 hits?
Bhartdarshan'is an internet-based travel agency wherein customer can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400.
a. What is the probability of getting more than 12,000 hits
