Choose the right answers, and provide reasons and calculation

To study the effect of change in price of a DVD ($) on the total profit (000, dollars), the analyst of an
electronic firm randomly selected 13 retail sales stores. She used the data on total profit (y) and DVD
price change (x) of these retail stores to get SSyy=298, and SSxx=44.16.and found the point prediction
ŷ = 27 – 2.5x of y. She chose α=0.01to make the decision. The point prediction ŷ = 27 – 2.5x of y
i. can be used to predict total profit from a given change in price of a DVD in the experimental region.
ii. will help the electronic firm to forecasting total profit if the firm continues its current sale strategies.
iii. will increase the total profit 2500 on the average if price of one DVD decrease by $1
iv. can be used for all of above

To determine which answers are correct, let's analyze each option:

i. The point prediction ŷ = 27 - 2.5x can be used to predict total profit from a given change in price of a DVD in the experimental region.

This statement is correct because the point prediction equation provides an estimate of the total profit (y) based on the change in price of a DVD (x).

ii. The point prediction ŷ = 27 - 2.5x will help the electronic firm to forecast total profit if the firm continues its current sale strategies.

This statement is also correct because the point prediction equation allows the electronic firm to estimate the total profit based on the change in price. By using this equation, the firm can forecast the total profit by considering their current sale strategies.

iii. The point prediction ŷ = 27 - 2.5x will increase the total profit by $2500 on average if the price of one DVD decreases by $1.

This statement is incorrect. The coefficient of -2.5 in the prediction equation represents the change in profit (y) per unit change in the price of a DVD (x). In this case, a $1 decrease in the price of one DVD would result in a decrease of $2.5 in the total profit, not an increase.

iv. The point prediction ŷ = 27 - 2.5x can be used for all of the above.

This statement is correct as it encompasses all the possibilities discussed in options i, ii, and iii.

Therefore, the correct answers are options i, ii, and iv.