I have a take home test I am working on. Any help would be appreciated. Professor does not teach from a book so am not sure how to apply this problem to the regression equation.
Thanks in advance. Problem below.
Cell Phone Mins= 3.5*cost + 25
where cell phone mins measure the number of minutes per month and cost is the dollar amount paid for the cell phone.
A) How many cell phone minutes are estimated to be used for someone who paid $95 for the cell phone?
B) Interpret the slope coefficient as an elasticity.
To solve this problem, you need to apply the given regression equation:
Cell Phone Mins = 3.5 * cost + 25
A) Calculate the estimated number of cell phone minutes for someone who paid $95 for the cell phone:
Substitute the value of the cost ($95) into the equation:
Cell Phone Mins = 3.5 * 95 + 25
Multiply the cost by 3.5:
Cell Phone Mins = 332.5 + 25
Add the two values together:
Cell Phone Mins = 357.5
Therefore, the estimated number of cell phone minutes for someone who paid $95 for the cell phone is 357.5 minutes.
B) Interpret the slope coefficient (3.5) as an elasticity:
The slope coefficient (3.5) represents the rate at which the number of cell phone minutes changes with respect to a one-unit increase in cost.
In this case, a one-unit increase in cost is equivalent to one dollar increase. Therefore, the slope coefficient represents the elasticity of cell phone minutes with respect to dollar cost.
Since the slope coefficient is positive (3.5), it indicates that there is a positive relationship between cost and the number of cell phone minutes. This means that as the cost increases, the number of cell phone minutes is expected to increase as well.
More precisely, for every one dollar increase in cost, the number of cell phone minutes is estimated to increase by 3.5 minutes.
To solve this problem, you need to apply the given regression equation to find the estimated number of cell phone minutes and interpret the slope coefficient as elasticity.
A) To find the estimated number of cell phone minutes for someone who paid $95 for the cell phone, simply substitute this value into the regression equation and solve for cell phone minutes:
Cell Phone Mins = 3.5 * Cost + 25
Substituting the cost value of $95 into the equation:
Cell Phone Mins = 3.5 * 95 + 25
Cell Phone Mins = 332.5 + 25
Cell Phone Mins = 357.5
So, the estimated number of cell phone minutes for someone who paid $95 for the cell phone is 357.5 minutes.
B) Now, let's interpret the slope coefficient as an elasticity. The slope coefficient in this case is 3.5. Elasticity measures the responsiveness of one variable (in this case, cell phone minutes) to changes in another variable (in this case, cost) while holding all other variables constant.
In this equation, the slope coefficient of 3.5 indicates that for every $1 increase in the cost of the cell phone, the estimated number of cell phone minutes increases by 3.5 minutes. This means that the number of cell phone minutes is relatively elastic to changes in cost, as a small change in the cost will result in a relatively large change in the estimated number of cell phone minutes.
Therefore, the slope coefficient of 3.5 can be interpreted as the elasticity of cell phone minutes with respect to cost, suggesting that a 1% increase in cost will result in approximately a 3.5% increase in the estimated number of cell phone minutes.