You are conducting a study on pie sales, and observed weekly sales figures from

Question

You are conducting a study on pie sales, and observed weekly sales figures from a bakery for n = 27 weeks. Let. the following variables denote your observations: y = Number of pies sold in a given week x_1 = price of a pie in dollars x_2 = amount spent on advertising, in dollars x_3 = a dummy variable that equals 1 if there is a holiday during the week, and 0 otherwise What do you predict would be the sign of each coefficient (b_i) in the regression line? Briefly explain each. Suppose b_1 = -2.35. Interpret this coefficient. Suppose b_3 = 37.8. Interpret this coefficient. Suppose you run a restricted regression using x_1 and x_3 and obtain R^2 = .867 and R^2 = .814. Furthermore, suppose the complete regression using x1, x_2, and x_3 yields R^2 = .893 and R^2 = .705. Which model do you think is better to use? Briefly explain.

Explanation / Answer

1.

B1 would be negitive sign as according to demand law, as price of a good increaases, Quantity decreases, soprice price and quantity ar negitively related.

B2 would be positive sign as advertizing spend increases, quantity demanded also increases, hence positive sign

B3 would be positive as on holidays there are sales more than normal days.

2.

B1 = -2.35 means when price increases by 1 unit, quantity demanded will decrease by 2.35 units

3

B3 = 37.8 means the sale on holidays is 37.8 units more than other week days during a week

4.

I think restricted regression using x1 and x3 is better to use because adjusted R-square decreases from 0.814 to 0.705 as we add x2 to the regression and adjusted R-squared provides an adjustment to the R-squared statistic such that an independent variable that has a correlation to Y increases adjusted R-squared and any variable without a strong correlation will make adjusted R-squared decrease. That is the desired property of a goodness-of-fit statistic.

Hence since goodness-of-fit will be more in case of restricted regression.

If you don't understand anything, then comment, I will revert back on the same.

And If you liked the answer then please do review the same. Thanks :)

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.