An electronics retailer used regression to find a simple model to predict sales growth in the first quarter of the new year (January through March). The model is good for 90 days, where *x* is the day. The model can be written as follows:

*ŷ* = 103.38 + 2.45*x*

 where *ŷ* is in thousands of dollars.

What would you predict the sales to be on day

(a) 60? (Enter an exact number as an integer, fraction, or decimal.)
 thousand dollars

(b) 90 ? (Enter an exact number as an integer, fraction, or decimal.)
 thousand dollars

To solve this problem, we will use the regression model provided:

\[
\hat{y} = 103.38 + 2.45x
\]

Here, \(\hat{y}\) represents the predicted sales in thousands of dollars, and \(x\) represents the day.

### Part (a) - Predict the sales on day 60:
For \(x = 60\):

\[
\hat{y} = 103.38 + 2.45(60)
\]

\[
\hat{y} = 103.38 + 147
\]

\[
\hat{y} = 250.38
\]

So, the predicted sales on day 60 would be **250.38 thousand dollars**.

### Part (b) - Predict the sales on day 90:
For \(x = 90\):

\[
\hat{y} = 103.38 + 2.45(90)
\]

\[
\hat{y} = 103.38 + 220.5
\]

\[
\hat{y} = 323.88
\]

So, the predicted sales on day 90 would be **323.88 thousand dollars**.

If you have any questions or want more details, feel free to ask. Here are five related questions:

1. How would you calculate the predicted sales for any other day within the first 90 days?
2. What is the significance of the coefficient 2.45 in this model?
3. How would the prediction change if the coefficient was negative?
4. Can this model be used for predicting sales after 90 days? Why or why not?
5. How would you assess the accuracy of this regression model?

**Tip:** In regression analysis, the coefficient of \(x\) represents the rate of change in the dependent variable (\(\hat{y}\)) for each unit change in the independent variable (\(x\)).

An electronics retailer used regression to find a simple model to predict sales growth in the first quarter of the new year (January through March). The model is good for 90 days, where x is the day. The model can be written as follows: ŷ = 103.38 + 2.45x, where ŷ is in thousands of dollars. What would you predict the sales to be on day (a) 60? (b) 90?

Learn how to predict sales growth using a linear regression model with the formula ŷ = 103.38 + 2.45x. This example covers predicting sales for days 60 and 90, demonstrating key concepts in linear regression and algebra. Suitable for high school students, Grades 10-12.

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