This is a Linear regression question, where I have a list of values for Sales ($Y$) and Property ($X$), I have calculated the Mean for both $Y$ and $X$, resulting in $Y=52.2$and $X=17$, I have calculated the Slope for this which is $m=2.5$ and the intercept $b=5.7$,
Question is suppose that for each $\$2$ of extra sales gives me $\$1$ of extra profit. How large would the slope need to be to make the product placement expenditure worth it?
I assume we are dealing with a break-even situation here?
A Sample of what I think I'm looking for is here
Explaining this in more detail:
If the slope is 1, then if I spend $\$1.00$ on advertising I get $\$1.00$ extra revenue but only $50%$ or $0.50 is extra profit. So my net position is -$1.00$+$0.50 so I am behind.
If the slope is 5, then if I spend $\$1.00$ on advertising I get $\$5.00$ extra revenue but only $50%$ or $2.50 is extra profit. So my net position is -$1.00+$2.50 so I am in front.
If the slope is 2.5, then if I spend $\$1.00$ on advertising I get $\$2.50$ extra revenue but only $50%$ or $1.25 is extra profit. So my net position is -$1.00+$1.25 so I am in front.
What value for the slope makes me break even?