Homework SourseThe following regression model has been proposed to predict
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.
Solution
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
![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\](/WebImages/26/the-following-regression-model-has-been-proposed-to-predict-1068523-1761559343-0.webp "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\")
