Chapter no. 05.pptx statistic analysis for masnagers

Chapter no. 05.pptx statistic analysis for masnagers

1. Statistical Analysis for Managers

2. Chapter No 5 Regression and Correlation Analysis Correlation Definition : Correlation refers to a statistical measure that describes the strength and direction of a relationship between two variables. It indicates whether and how strongly the variables are related. Positive correlation: When one variable increases, the other also increases (e.g., height and weight in general). Negative correlation: When one variable increases, the other decreases (e.g., speed of a car and the time taken to reach a destination). No correlation: When the variables do not show any consistent pattern in their relationship.

3. Steps to solve? Correlation Coefficient Coefficient of Determination Regression line Standard Error Standard Error of determination Calculation of Standard Error Hypothesis testing of OLS Estimates Scattered Diagram

4. Correlation Coefficient The correlation coefficient is a statistical measure that quantifies the strength and direction of a relationship between two variables. It indicates how well the variations in one variable are associated with variations in another. The value of the correlation coefficient reflects how strongly the two variables are related. Values closer to 1 or -1 indicate a strong relationship, while values closer to 0 indicate a weak relationship.

5. Coefficient of Determination The coefficient of determination, often denoted as “square of r “ is a statistical measure that explains how much of the variance in one variable can be explained by the variance in another variable. It is derived from the correlation coefficient and is used primarily in the context of regression analysis to assess how well the regression model fits the data.

6. Regression Analysis Regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the outcome or response variable) and independent variables (often called regressors, predictors, covariates, explanatory variables or features).

7. Hypothesis testing of OLS Estimates Hypothesis testing in the context of Ordinary Least Squares (OLS) estimates involves determining whether the estimated coefficients of the regression model are statistically significant. The process generally includes the following steps: 1. Formulate the Hypotheses: - Null Hypothesis (H0): The coefficient of the predictor variable (beta) is equal to zero (no effect). - Alternative Hypothesis (H1): The coefficient of the predictor variable is not equal to zero (there is an effect).

8. Continued: 2. Estimate the Model: Use OLS to estimate the regression model and obtain the coefficients. 3. Calculate the Test Statistic: The test statistic for the hypothesis test is typically calculated using the formula: t = (b - 0) / SE(b) where b is the estimated coefficient and SE(b) is the standard error of the coefficient.

9. Question no 01 X Y 2 4 5 6 9 3 3 1 1 2 Find Correlation coefficient its determination by using Regression line.

10. Question no 02 Find Correlation coefficient its determination by using Regression line. X Y 10 15 12 20 15 22 18 25 20 37

11. Question no 03 X Y 20 40 30 30 40 22 60 15 80 10