The following regression model has been proposed to predict sales at a furniture

Question

The following regression model has been proposed to predict sales at a furniture store. ^ y (hat) = 10 - 4x1 + 7x2 + 18x3
Where x1 = competitor's previous day's sales (in $1,000s) x2 = population within 1 mile (in 1,000s) x3 = 1 if any form of advertising was used, 0 if otherwise ^ Y(hat)= sales (in $1,000s)
A. Fully interpret the meaning of coefficient of x3 B. Predict sales (in dollars) for a store with competitor's previous day's sale of $3,000, a population of 10,000 within 1 mile, and six radio advertisements.
The following regression model has been proposed to predict sales at a furniture store. ^ y (hat) = 10 - 4x1 + 7x2 + 18x3
Where x1 = competitor's previous day's sales (in $1,000s) x2 = population within 1 mile (in 1,000s) x3 = 1 if any form of advertising was used, 0 if otherwise ^ Y(hat)= sales (in $1,000s)
A. Fully interpret the meaning of coefficient of x3 B. Predict sales (in dollars) for a store with competitor's previous day's sale of $3,000, a population of 10,000 within 1 mile, and six radio advertisements.
^ y (hat) = 10 - 4x1 + 7x2 + 18x3 ^ y (hat) = 10 - 4x1 + 7x2 + 18x3
Where x1 = competitor's previous day's sales (in $1,000s) x2 = population within 1 mile (in 1,000s) x3 = 1 if any form of advertising was used, 0 if otherwise ^ Y(hat)= sales (in $1,000s)
A. Fully interpret the meaning of coefficient of x3 B. Predict sales (in dollars) for a store with competitor's previous day's sale of $3,000, a population of 10,000 within 1 mile, and six radio advertisements.

Explanation / Answer

A. Coefficient of X3 = 18

X3: 1 if any advertisement made,

       0 otherwise

So Sales of a store will get increased by 18,000 $ if an advertising used. If no advertise no extra sales of store.

B. X1=3, X2=10 & X3=1 as units are in 1,000s in the given model

Y_hat = 10 - (4*3) + (7*10) + (18*1) = 86 (in $1,000s)

Predicted sales of the store is $86,000

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