# Regression Analysis-Case Solution Step 1 **Understanding the** Princess Foods to know if is a relationship the amount a household on prepared foodsdependent variable) two independent variables- Family size- Gross monthly We will usemultiple linear regression to analyze this--- ## Step2: ** the Data** data columns are: - **Y:** Dollars spent on prepared food (dependent variable) - **X₁:** Family size - **X₂:** Gross monthly income --- ## Step 3: **Set Up the Regression Equation** The regression equation will be: \[ Y = \beta_ + \beta_1 X_1 + \beta_2 X_2 + \varepsilon \] Where: - \(Y\) = Dollars spent on prepared food - \(X_1\) = Family size - \(X_2\) = Gross monthly income --- ## Step 4: **Input Data into Excel** 1. Enter data into three columns in Excel: | Dollars spent | Family size | Gross monthly income | 2. Click **Data** → **Data Analysis** → **Regression**. 3. Set: - **Y Range:** Dollars spent on prepared food - **X Range:** Family size and gross monthly income - Check **Labels** if you include headers. - Output to a new worksheet. --- ## Step 5: **Get the Regression Output** Here is a sample of what you would get (values are for illustration; use Excel for exact results): | Coefficient | Estimate | |----------------|------------| | Intercept | 120.00 | | Family size | 45.00 | | Gross income | .09 | (The actual coefficients may vary depending on the calculation.) --- ## Step 6: **Regression Equation** Suppose the output is: \[ \text{Dollars spent} = 120 + 45 \cdot (\text{Family size}) + .09 \cdot (\text{Gross income}) \] --- ## Step 7: **Goodness of Fit** Check the **R-squared** value in the output (say, for example, \( R^2 = .78 \)). - **R-squared** tells us how much of the variation in dollars spent can be explained by family size and income. - \( R^2 = .78 \) means **78%** of the variation is explained by the model. --- ## Step 8: **Interpretation and Memo** ### **Interpretation** - **Family Size:** For each additional family member, spending on prepared foods increases by about $45 (holding income constant). - **Gross Income:** For every additional $1 in income, spending increases by $.09 (holding family size constant). ### **Goodness of Fit** - The model fits the data well (if \( R^2 \) is high). ### **How the Data Can Be Used** - **Marketing:** Target larger families and higher-income households with new product lines. - **Product Development:** Consider meal kits and frozen foods tailored to larger families and higher-income segments. - **Pricing:** Adjust pricing strategies based on household income and size. --- ## Final Answer: **Sample Memo** --- ### **To:** Princess Foods Marketing Team ### **From:** [Your Name], Data Analyst ### **Subject:** Regression Analysis of Household Prepared Food Spending #### **Summary** A regression analysis was conducted to determine the relationship between household spending on prepared foods, family size, and gross monthly income. The model is: \[ \text{Dollars spent} = 120 + 45 \cdot (\text{Family size}) + .09 \cdot (\text{Gross income}) \] #### **Findings** - **Family size** and **income** both have a positive impact on spending. - The model explains about **78%** of the variation in spending. - Larger families and those with higher incomes spend more on prepared foods. #### **Recommendations** - Focus marketing and new product development on larger and higher-income households. - Use these insights to refine pricing and promotional strategies. --- **Note:** Please use Excel to get the actual coefficients and R-squared value. Substitute them in the memo above. --- **If you want, I can walk you through the Excel steps in more detail!**