The purpose of this activity is to investigate the correlation between variables. You will study the relationships between time, average hours worked, and average earnings for U.S. production workers over a period of 30 years.

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The table below lists the average number of hours worked in a week and the average weekly earnings for U.S. production workers from 1967 to 1996. (The World Almanac 1998)

Year	Weekly Hour	Weekly Earnings
1967	38.0	$101.84
1968	37.8	$107.73
1969	37.7	$114.61
1970	37.1	$119.83
1971	36.9	$127.31
1972	37.0	$136.90
1973	36.9	$145.39
1974	36.5	$154.76
1975	36.1	$163.53
1976	36.1	$174.45
1977	36.0	$189.00
1978	35.8	$203.70
1979	35.7	$219.91
1980	35.3	$235.10
1981	35.2	$255.20
1982	34.8	$267.26
1983	35.0	$280.70
1984	35.2	$292.86
1985	34.9	$299.09
1986	34.8	$304.85
1987	34.8	$312.50
1988	34.7	$322.02
1989	34.6	$334.24
1990	34.5	$345.35
1991	34.3	$353.98
1992	34.4	$363.61
1993	34.5	$373.64
1994	34.7	$385.86
1995	34.5	$394.34
1996	34.4	$406.26

Part 1

1. Construct a scatter diagram and comment on the relationship, if any, between the variables Weekly Hoursand Weekly Earnings.
2. Determine and interpret the correlation for hours worked and earnings. The CORREL function in Excel will be helpful. Based upon the value of the correlation, is your answer to the previous question reasonable?
3. Based upon the data given, estimate the average weekly earnings for a workweek of 33.8 hours. How confident are you in your estimate?You should use a linear regression model to make your prediction. To create the linear regression model in Excel, right-click on a data point and click Add Trendline... In the options that display on the right, click Display Equation on chart.
4. Increase/decrease in weekly hours: a) For a production worker who wishes to increase weekly earnings, would you recommend a decrease in hours worked per week? Why or why not? b) Does a decrease in hours worked cause an increase in weekly pay? c) What other variables could contribute to an increase in weekly pay?

Part 2

Using the same table of data:

1. Construct a scatter diagram and comment on the relationship, if any, between the variables Year and Hours Worked.
2. Determine and interpret the correlation for the year and hours worked. Based upon the value of the correlation, is your answer to the previous question reasonable?
3. Based upon the data given, estimate the average weekly hours worked this year. How confident are you in your estimate?You should use a linear regression model to make your prediction.
4. Assuming a linear correlation between these two variables, what will happen to the average weekly hours worked in the future? Is it possible for this pattern to continue indefinitely? Explain.

Part 3

Use the same table of data:

1. Construct a scatter diagram and comment on the relationship, if any, between thevariables Year and Weekly Earnings.
2. Determine and interpret the correlation for the year and weekly earnings. Based upon the value of the correlation, is your answer to the previous question reasonable?
3. Based upon the data given, estimate the average weekly earnings this year. How confident are you in your estimate?You should use a linear regression model to make your prediction.
4. Assuming a linear correlation between these two variables, what will happen to the average weekly earnings in the future? Is it possible for this pattern to continue indefinitely? Explain.