Davis Stores sells clothing in 15 stores located around the southwestern United States. The managers at Davis are considering expanding by opening new stores and are interested in estimating costs in potential new locations. They believe that costs are driven in large part by store volume measured by revenue. The following data were collected from last year’s operations (revenues and costs in thousands of dollars).

Store Revenues Costs

101 $4,140 $4,274

102 2,267 2,974

103 5,798 5,241

104 4,062 4,098

105 2,974 3,796

106 4,103 3,459

107 6,934 5,089

108 1,839 2,574

109 5,616 4,848

110 3,348 3,079

111 3,966 4,279

112 4,790 3,280

113 3,592 2,676

114 4,977 4,735

115 2,324 3,046

Simple regression results from the data of Davis Stores are as follows.

Equation:

Store costs = $1,693. 5 + (Revenue × 52. 8%)

Statistical data

Correlation coefficient 0. 838

R2 0. 702

Required:

a. Estimate store costs for a store with revenue of $2. 9 million.

b. What percentage of the variation in store costs is explained by the independent variable?

To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the problem.

From the linear regression, the correlation coefficient is also found, and explains the percentage of variation that is explained by the independent variable.

7

In the context of this problem, the store costs are given as a function of the revenue as follows:

Store costs = $1,693. 5 + 0.528(Revenue)

Above, we used the decimal equivalent of the percentage.

Hence, for a revenue of 2.9 million = 2900 thousand, the store costs are as follows:

Store costs = 1693.5 + 0.528(2900) = 3224.7 = $3,224,700.

Due to the correlation coefficient of 0.838, 83.8% of variation in store costs is explained by the independent variable.

More can be learned about linear regression at https://brainly.com/question/22992800

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