Correlation and Confidence Intervals
Explores correlation coefficients, confidence intervals, and statistical reliability.
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Correlation and Confidence Intervals
A car dealer is using the number of years customers have owned their vehicles to predict how
long it will be before they elect to replace them. The correlation between the two is rxy = -.723
(the longer they have owned their present vehicles, the more quickly they are expected to replace
them). The other relevant data are as follows for 32 customers:
Based on the information above, answer the following questions:
1. How long is the time to expected replacement for a customer who has owned a vehicle
6.5 years?
2. Calculate .95 and .99 confidence intervals and explain your results.
3. How will a larger standard deviation in the criterion variable affect the width of the
confidence intervals? Why?
4. Guided Response: Review several of your classmates’ postings. Respond to at least two
classmates by commenting on whether or not you think there is a larger difference for the
standard deviation. Explain how this data might impact business decision-making.
1. How long is the time to expected replacement for a customer who has owned a vehicle
6.5 years?
The expected time replacement for a customer who has owned a vehicle 6.5 years is:
4.965 -0.5946*6.5 =1.1001 years.
2. Calculate .95 and .99 confidence intervals and explain your results.
32* =32*1.338*1.338 =57.2878
RSS (regression sum of squares) = (rxy)2*TSS = (-0.723)2*57.2878 = 29.946
ESS (error sum of squares) = TSS-RSS =57.2878-29.946 = 27.3418
Standard error σe = = = 0.9547
Predicted standard error value SE ( ) =σe
= 0.9547 = 0.0726
A car dealer is using the number of years customers have owned their vehicles to predict how
long it will be before they elect to replace them. The correlation between the two is rxy = -.723
(the longer they have owned their present vehicles, the more quickly they are expected to replace
them). The other relevant data are as follows for 32 customers:
Based on the information above, answer the following questions:
1. How long is the time to expected replacement for a customer who has owned a vehicle
6.5 years?
2. Calculate .95 and .99 confidence intervals and explain your results.
3. How will a larger standard deviation in the criterion variable affect the width of the
confidence intervals? Why?
4. Guided Response: Review several of your classmates’ postings. Respond to at least two
classmates by commenting on whether or not you think there is a larger difference for the
standard deviation. Explain how this data might impact business decision-making.
1. How long is the time to expected replacement for a customer who has owned a vehicle
6.5 years?
The expected time replacement for a customer who has owned a vehicle 6.5 years is:
4.965 -0.5946*6.5 =1.1001 years.
2. Calculate .95 and .99 confidence intervals and explain your results.
32* =32*1.338*1.338 =57.2878
RSS (regression sum of squares) = (rxy)2*TSS = (-0.723)2*57.2878 = 29.946
ESS (error sum of squares) = TSS-RSS =57.2878-29.946 = 27.3418
Standard error σe = = = 0.9547
Predicted standard error value SE ( ) =σe
= 0.9547 = 0.0726
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Subject
Statistics