Correlation and Confidence Intervals

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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 σ e = = = 0.9547 Predicted standard error value SE ( ) = σ e = 0.9547 = 0.0726
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