2. In the regression equation, the value that gives the amount by which Y changes for one unit in X is called the (a) coefficient of correlation. (b) coefficient of determination. (c) slope. (d) intercept.

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### Understanding Regression Equations

In regression analysis, we often examine how changes in one variable lead to changes in another. This concept is captured in the regression equation, which is fundamental to statistical and data analysis.

**Question:**

In the regression equation, the value that gives the amount by which Y changes for one unit in X is called the:

- (a) coefficient of correlation.
- (b) coefficient of determination.
- (c) slope.
- (d) intercept.

**Explanation:**

- **Coefficient of Correlation (a):** This measures the strength and direction of a linear relationship between two variables, typically denoted as 'r'.

- **Coefficient of Determination (b):** Denoted as 'R²', this value indicates the percentage of the variance in the dependent variable that is predictable from the independent variable.

- **Slope (c):** This is the correct answer. In the context of a regression equation, the slope represents the change in the dependent variable (Y) for a one-unit change in the independent variable (X).

- **Intercept (d):** This is the point where the regression line crosses the Y-axis, representing the value of Y when X is zero.
Transcribed Image Text:### Understanding Regression Equations In regression analysis, we often examine how changes in one variable lead to changes in another. This concept is captured in the regression equation, which is fundamental to statistical and data analysis. **Question:** In the regression equation, the value that gives the amount by which Y changes for one unit in X is called the: - (a) coefficient of correlation. - (b) coefficient of determination. - (c) slope. - (d) intercept. **Explanation:** - **Coefficient of Correlation (a):** This measures the strength and direction of a linear relationship between two variables, typically denoted as 'r'. - **Coefficient of Determination (b):** Denoted as 'R²', this value indicates the percentage of the variance in the dependent variable that is predictable from the independent variable. - **Slope (c):** This is the correct answer. In the context of a regression equation, the slope represents the change in the dependent variable (Y) for a one-unit change in the independent variable (X). - **Intercept (d):** This is the point where the regression line crosses the Y-axis, representing the value of Y when X is zero.
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In regression equation, coefficient of x i.e. slope tells us if we increase the value of x by one unit, y increases by the amount that is equal to the slope.

 

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