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A grocery store wants to examine the relationship between the sales amounts each day at two different locations, store A and store B. The sales amount each day, in dollars, was recorded for 10 days at each store. The least-squares regression line is yˆ=−3,000+1.2x y ^ = − 3 ,000 + 1.2 x , where x x represents the sales amounts each day at store A and y y represents the sales amounts each day at store B. If the mean of the 10 sales amounts for store B is $45,000, what is the mean of the 10 sales amounts for store A?

Respuesta :

calculista

Answer:

The mean of the 10 sales amounts for store A is $40,000

Step-by-step explanation:

The  least-squares regression line is

[tex]y=-3,000+1.2x[/tex]

where

x represents the sales amounts each day at store A

y represents the sales amounts each day at store B

we have

y=$45,000

substitute the value of y in the linear equation and solve for x

[tex]45,000=-3,000+1.2x[/tex]

[tex]1.2x=45,000+3,000[/tex]

[tex]1.2x=48,000[/tex]

[tex]x=40,000[/tex]

therefore

The mean of the 10 sales amounts for store A is $40,000

fichoh

The mean of the 10 sales made at store A using the regression equation is $40,000

The regression model given :

  • y = - 3000 + 1.2x

  • y = sales amount per day at store A
  • x = sales amount per day at store B

The mean amount for 10 sales at store B = $45,000 ; then y = $45,000

Substitute y = 45000 into the regression equation :

Hence, we have ;

45000 = -3000 + 1.2x

Add 3000 to both sides

45000 + 3000 = 1.2x

48000 = 1.2x

Divide both sides by 1.2

48000/1.2 = x

x = $40,000

Therefore, the mean sales at store A will be $40,000

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