Question

A really cool ice cream store owner developed a model to relate to his ice cream shop sales (Y) to the amount of advertising dollars he spent (X1) to the number of extra smiling faces he put on staff for the day (X2) to the degrees in average daily temperature above 70 degrees (X3) ((At 70 degrees X3=)(at 70 degrees X3=0 )

The multiple regression equation for this model is: Ŷ=$5000 + $500(X1) + $200(X2) + 100(X3)
where:
Ŷ = daily sales in ($)
X1= advertising dollars spent in $100 increments (for $100 in advertising dollars spent X1 =1)
X2= extra staff member in increments of 1 up to 4. Above 4 no more added sales.
X3= average daily temperature above or below 70 degrees in one degree increments, (at 70 degrees X3=0)
What is the y-intercept (a)
A.$5000
B.$200
C.$100
D.None of the above

Answer 1

The y-intercept of the multiple regression equation is $5000.

Step-by-step explanation:

The y-intercept of the multiple regression equation for the ice cream shop sales model is $5000. In the equation Ŷ = $5000 + $500(X1) + $200(X2) + 100(X3), the coefficient of the constant term ($5000) represents the y-intercept, which is the value of Y when X1, X2, and X3 are all 0.

Answer 2

The y-intercept in the given multiple regression equation is $5000, corresponding to the constant term in the equation when all other variables are zero.

Step-by-step explanation:

In the multiple regression equation provided, the y-intercept is the constant term when all other variables are equal to zero. In this case, the equation is ÂŽ=$5000 + $500(X1) + $200(X2) + $100(X3). Here, the y-intercept would be the value of ÂŽ when X1, X2, and X3 are all zero. Looking at the equation, it's evident that the y-intercept is $5000. Therefore, the correct answer is A. $5000.