Explain a regression analysis

Interpretation of Results:

1. Intercept (β₀): 10

• Interpretation: The intercept represents the predicted value of the dependent variable (sales) when the independent variable (advertising spend) is zero. In this case, if there is no advertising spend, the model predicts that sales would be 10 units (e.g., 10,000 dollars).

2. Slope (β₁): 2.5

• Interpretation: The slope indicates the expected change in the dependent variable (sales) for a one-unit increase in the independent variable (advertising spend). Here, for every additional dollar spent on advertising, sales are expected to increase by 2.5 units (e.g., an additional 2,500 dollars in sales).

3. R² (R-squared): 0.85

• Interpretation: The R² value of 0.85 indicates that 85% of the variability in the dependent variable (sales) can be explained by the independent variable (advertising spend). This suggests that the model fits the data well, with a strong linear relationship between advertising spend and sales.

4. p-value for Slope: 0.001

• Interpretation: The p-value for the slope is 0.001, which is significantly smaller than the typical significance level of 0.05. This indicates that there is strong evidence to reject the null hypothesis that the slope is zero. In other words, advertising spend is statistically significant in predicting sales.

5. Standard Error of Estimate: 5

• Interpretation: The standard error of the estimate is a measure of the average distance between the observed values and the predicted values from the regression model. A smaller value suggests a better fit of the model. In this case, the standard error of 5 indicates that, on average, the predicted sales may vary by 5 units from the actual observed sales.