Question

Regression analysis was applied between sales (in $1000) and advertising (in $100), and the following regression function was obtained: y=80+6.2x. Based on the above estimated regression line, if advertising is $10,000, then what is the point estimate for sales (in dollars)?

a. $62,080
b. $142,000
c. $700
d. $700,000
e. None of the above

Answer 1

The point estimate for sales with $10,000 spent on advertising is calculated using the regression equation y=80+6.2x, resulting in an estimated sales figure of $700,000. Correct option is d. $700,000

Step-by-step explanation:

The question presented involves interpreting a linear regression equation to predict sales based on advertising expenses. The regression equation is given as y=80+6.2x, where y is the sales in $1000 and x is the advertising in $100. To find the point estimate for sales when the advertising is $10,000, one must first convert the advertising amount from dollars to hundreds of dollars by dividing by 100, which gives us x = 100. We then substitute x into the regression equation.

Step-by-step calculation:

1. Convert advertising amount to the scale used in the regression equation: $10,000 / $100 = 100.
2. Substitute x into the regression equation: y = 80 + 6.2(100).
3. Perform the multiplication: 6.2 * 100 = 620.
4. Add the intercept: 620 + 80 = 700.
5. Convert y back into dollars (since y is in $1000): 700 * $1000 = $700,000.

Therefore, the point estimate for sales, when advertising is $10,000, is $700,000.