Regression Analysis Statistics and Interpretation Explained

Regression Statistics

• Multiple R: Coefficient of correlation (0.099). 9.9% of variability in Y is connected with 9.95% of variability in X.
• R-squared: Coefficient of determination (0.0099). 0.99% of variance in Y is explained by our regression model.
• Standard Error: The prediction of Y made using our model will differ from reality by approximately [number].
• Observations: The model contains [x] units.

Intercept (B0)

Coefficients: If we do not take X into consideration, Y will be [..].

T-stat: Calculated as (coefficient / standard error).

P-value: Level of risk is nearly 0, indicating a 99.99% probability.

Lower/Upper 95%: We are 95% confident that our coefficient B0 falls between 27.4 and 30.8.

Age (B1)

Coefficients: If X increases by 1 year, Y will increase by [....].

T-stat: [....].

P-value: The relationship between X and Y is statistically significant at a 95% confidence level (1 - p-value).

Lower/Upper 95%: We are 95% confident that our coefficient B1 falls between 0.0000005 and 0.077.

Descriptive Statistics

• Mean Absolute Deviation: The average absolute difference between the value in our sample and the mean. A higher value indicates a more spread-out sample.
• Standard Deviation: The average difference between revenue in a given year and the mean.
• Coefficient of Variation: Compares the standard deviation of monthly stock prices to the mean. A higher coefficient indicates greater volatility.
• Coefficient of Skewness: A positive coefficient indicates a positively skewed distribution (e.g., a small number of units accepting many candidates).

Regression Application

B1 Interpretation: If X increases by 1,000, Y will increase by [....].

Regression Formula: A person earning [....] would spend [....] on Y according to our model.

Inferences and Model Validation

Inferences Concerning the Slope: If the t-test (tt) is greater than the critical value (tc), the relationship is statistically significant (reject the null hypothesis). If tt < tc, we accept the null hypothesis.

Coefficient of Determination (R-squared): This model explains [R2 result] of the variance in Y (values range from 0 to 1).

Correlation Coefficient: 98% of variability in Y is connected to 98% of variability in advertising X. This indicates a very strong, positive relationship between the two variables.