After running regression on the sales' data of a chain department store, we get the following model:

y=13.2+6.1x1+0.3x2+1.2Q1−1.7Q2+2.6Q3

where:

*y* is sales in million dollars

*x1* is the store size in 1000 sq ft

*x2* is the number of years the store has been open, and

*Qi*'s are dummy variables that is 1 if quarter = *i* ; and 0 otherwise.

In answering the following questions, pay attention to **units** of x1 and y, and **signs** of coefficients.         How to solve in excel: What is the expected sales difference between Q2 and Q3? Which quarter is expected to be higher?

Group of answer choices

$900,000, Q2

$4.3 million, Q3

$900,000, Q3

$4.3 million, Q2

We are given the regression model:

\[
y = 13.2 + 6.1x_1 + 0.3x_2 + 1.2Q_1 − 1.7Q_2 + 2.6Q_3
\]

where:

- $ y $ is the sales in million dollars.
- $ x_1 $ is the store size in 1000 square feet.
- $ x_2 $ is the number of years the store has been open.
- $ Q_i $ are dummy variables representing the quarters (1 for the specified quarter, 0 otherwise).

### Step-by-Step Approach:

To calculate the expected sales difference between Q2 and Q3, we need to look at the coefficients associated with these quarters:

- Coefficient for $ Q_2 = -1.7 $
- Coefficient for $ Q_3 = 2.6 $

The sales difference between Q2 and Q3 is determined by the difference in their coefficients. The rest of the variables (store size, years open) are not relevant for this comparison since they remain constant across quarters.

\[
\text{Sales Difference} = \text{Coefficient of } Q_3 - \text{Coefficient of } Q_2
\]

\[
\text{Sales Difference} = 2.6 - (-1.7) = 2.6 + 1.7 = 4.3 \text{ million dollars}
\]

Thus, the expected sales difference between Q2 and Q3 is **$4.3 million**.

### Which quarter is expected to be higher?

Since the coefficient for $ Q_3 $ (2.6) is larger than the coefficient for $ Q_2 $ (-1.7), the sales in Q3 are expected to be higher.

### Conclusion:

- The expected sales difference between Q2 and Q3 is **$4.3 million**.
- **Q3** is expected to have higher sales.

Thus, the correct answer is:

**$4.3 million, Q3.**

### Would you like detailed steps on how to perform these calculations in Excel?

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Here are five questions to extend this topic:

1. How does the size of the store ($x_1$) affect sales according to the model?
2. What would be the expected sales for a store in Q1?
3. How would the regression model change if you added a fifth dummy variable for a new quarter?
4. Can this model predict sales for a brand-new store? Why or why not?
5. How would negative coefficients for quarters impact sales predictions?

**Tip:** In regression models, dummy variables allow categorical data (like quarters) to be included as numerical predictors.

After running regression on the sales' data of a chain department store, we get the following model: y = 13.2 + 6.1x1 + 0.3x2 + 1.2Q1 − 1.7Q2 + 2.6Q3 where: *y* is sales in million dollars *x1* is the store size in 1000 sq ft *x2* is the number of years the store has been open, and *Qi*'s are dummy variables that is 1 if quarter = *i* ; and 0 otherwise. How to solve in Excel: What is the expected sales difference between Q2 and Q3? Which quarter is expected to be higher?

Learn how to calculate the expected sales difference between Q2 and Q3 in a department store using a regression model. Understand the impact of dummy variables and interpret regression coefficients. This step-by-step solution provides insights into sales forecasting techniques.

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