Question 1198680
## 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.