Math Problem Statement

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.

Solution

The estimated regression equation is of the form:

y^=b0+b1x\hat{y} = b_0 + b_1 x

Where:

  • y^\hat{y} is the estimated revenue (in thousands of dollars),
  • xx is the month,
  • b0b_0 is the intercept,
  • b1b_1 is the slope of the line (representing the change in revenue per month).

From the regression output:

  • The intercept b0=470.5033b_0 = 470.5033,
  • The slope b1=28.5728b_1 = 28.5728.

Thus, the estimated regression equation is:

y^=470.5033+28.5728x\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 b1b_1 in the context of this problem?
  2. What is the significance of the intercept b0b_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 R2R^2 is to 1, the better the model explains the variability of the response variable.

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Math Problem Analysis

Mathematical Concepts

Linear Regression
Statistics
Algebra

Formulas

ŷ = b₀ + b₁x (Regression Equation)
R² (Coefficient of Determination)

Theorems

Least Squares Estimation

Suitable Grade Level

College Level, Advanced High School (Grades 11-12)