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Regression analysis was applied between sales (in $1,000) and advertising (in $100), and the following regression function was obtained.y-hat = 87 + 7.8 xBased on the above estimated regression line, if advertising is $11,924, then the point estimate for sales (in dollars) is

Question

Regression analysis was applied between sales (in 1,000)andadvertising(in1,000) and advertising (in 100), and the following regression function was obtained.y-hat = 87 + 7.8 xBased on the above estimated regression line, if advertising is $11,924, then the point estimate for sales (in dollars) is

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Solution

The regression function given is y-hat = 87 + 7.8x. Here, 'x' represents the advertising cost in 100andyhatrepresentstheestimatedsalesin100 and 'y-hat' represents the estimated sales in 1,000.

First, we need to convert the advertising cost from dollars to hundreds of dollars, because the regression function uses hundreds of dollars.

So, x = 11,924/11,924 / 100 = 119.24

Now, we can substitute x = 119.24 into the regression function:

y-hat = 87 + 7.8 * 119.24

Calculate the value:

y-hat = 87 + 930.072 = 1017.072

This is in thousands of dollars, so convert it back to dollars:

Estimated sales = 1017.072 * 1,000=1,000 = 1,017,072

So, the point estimate for sales, given an advertising cost of 11,924,isapproximately11,924, is approximately 1,017,072.

This problem has been solved

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