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Interpret the Slope and the Y-Intercept of the Least-Squares Regression y^=β0+β1x\hat { y } = \beta _ { 0 } + \beta _ { 1 } \mathrm { x }

Question 95

Multiple Choice

Interpret the Slope and the y-intercept of the Least-Squares Regression Line
-A large national bank charges local companies for using its services. A bank official reported the results of a regression analysis designed to predict the bank's charges (y) , measured in dollars per month, for services rendered to local companies. One independent variable used to predict service charge to a company is the company's sales revenue (x) , measured in millions of dollars. Data for 21 companies who use the bank's services were used to fit the model, y^=β0+β1x\hat { y } = \beta _ { 0 } + \beta _ { 1 } \mathrm { x } . The results of the simple linear regression are provided below.
y^=2,700+20x,s=65,2-tailed p-value =0.064 (for testing β1 )  \hat { \mathrm { y } } = 2,700 + 20 \mathrm { x } , \mathrm { s } = 65,2 \text {-tailed p-value } = 0.064 \text { (for testing } \beta _ { 1 } \text { ) }
Interpret the estimate of β0\beta _ { 0 } , the yy -intercept of the line.


A) There is no practical interpretation since a sales revenue of $0\$ 0 is a nonsensical value.
B) All companies will be charged at least $2,700\$ 2,700 by the bank.
C) About 95%95 \% of the observed service charges fall within $2,700\$ 2,700 of the least squares line.
D) For every $1\$ 1 million increase in sales revenue, we expect a service charge to increase $2,700\$ 2,700 .

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