Consider the following monthly revenue data for an up-and-coming technology company.

Sales Data
Month	Revenue (Thousands of Dollars)	Month	Revenue (Thousands of Dollars)
1
325
10
819
2
547
11
831
3
539
12
848
4
580
13
860
5
640
14
863
6
699
15
879
7
697
16
903
8
708
17
912
9
797
18
908


The summary output from a regression analysis of the data is also provided.

Regression Statistics
Multiple R	0.93482589
R Square	0.873899444
Adjusted R Square	0.86601816
Standard Error	59.72646232
Observations	18

ANOVA
df
SS
MS
F
Regression	1
395,546.939628
395,546.939628
110.8828667
Residual	16
57,076.004816
3567.250301
Total	17
452,622.944444

Coefficients	Standard Error	t
 Stat	P-value
Intercept	470.50326797
29.37121675
16.01919566
2.83992E-11
Month	28.57275542
2.713437989
10.530093385
1.33255E-08
Step 1 of 3 :  Write the estimated regression equation using the least squares estimates for b0
 and b1
. Round to four decimal places, if necessary.


The estimated regression equation is of the form:

\[
\hat{y} = b_0 + b_1 x
\]

Where:
- \( \hat{y} \) is the estimated revenue (in thousands of dollars),
- \( x \) is the month,
- \( b_0 \) is the intercept,
- \( b_1 \) is the slope of the line (representing the change in revenue per month).

From the regression output:
- The intercept \( b_0 = 470.5033 \),
- The slope \( b_1 = 28.5728 \).

Thus, the estimated regression equation is:

\[
\hat{y} = 470.5033 + 28.5728x
\]

This equation predicts the company's revenue based on the month.

Would you like more details or have any further questions?

Here are 5 related questions:
1. How do you interpret the slope \( b_1 \) in the context of this problem?
2. What is the significance of the intercept \( b_0 \) for this company’s revenue?
3. What does the R Square value tell us about the fit of the model?
4. How would you calculate the predicted revenue for month 20?
5. What is the purpose of the Standard Error in regression analysis?

**Tip:** The closer the value of \( R^2 \) is to 1, the better the model explains the variability of the response variable.

Consider the following monthly revenue data for an up-and-coming technology company.

Sales Data
Month Revenue (Thousands of Dollars) Month Revenue (Thousands of Dollars)
1 325
2 547
3 539
4 580
5 640
6 699
7 697
8 708
9 797
10 819
11 831
12 848
13 860
14 863
15 879
16 903
17 912
18 908

The summary output from a regression analysis of the data is also provided.

Step 1 of 3: Write the estimated regression equation using the least squares estimates for b0 and b1. Round to four decimal places, if necessary.

Learn how to estimate the regression equation for an up-and-coming technology company using monthly revenue data. This problem demonstrates the use of least squares estimation and explains the regression output, including R² and standard error. Suitable for advanced high school or college-level students.

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