Advanced Regression(KA/SAP/U15AdvancedRegression)

Unit 15: Advanced Regression (Inference and Transforming)

1. Inference about Slope

In regression analysis, the slope of the regression line represents the average change in the response variable for each one-unit increase in the explanatory variable.
Inference about slope involves determining whether the observed relationship between variables is statistically significant or could have occurred by random chance.

• Null Hypothesis (H₀): The true slope is zero (no relationship).
• Alternative Hypothesis (H_a): The true slope is not zero (there is a relationship).

We use a t-test to test the significance of the slope. The test statistic is:
t = (b - 0) / SE_b
where b is the sample slope and SE_b is its standard error.

Quiz: Inference about Slope

1. What does the slope of a regression line represent?

--Select-- The average change in the response variable for each unit increase in the explanatory variable The intercept of the regression line The correlation coefficient

Correct! The slope shows the average change in the response variable for each unit increase in the explanatory variable.

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2. What is the null hypothesis when testing the significance of a regression slope?

--Select-- The true slope is zero The true slope is positive The true slope is negative

Correct! The null hypothesis is that the true slope is zero.

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2. Nonlinear Regression

Nonlinear regression is used when the relationship between variables cannot be adequately described by a straight line. Instead, the data may follow a curve, such as exponential, logarithmic, or polynomial patterns.

• Exponential regression: Models data that grows or decays at a constant percentage rate.
• Logarithmic regression: Models data that increases quickly and then levels off.
• Polynomial regression: Models data with curves, such as parabolas.

Nonlinear regression finds the best-fitting curve by minimizing the differences between observed and predicted values.

Quiz: Nonlinear Regression

1. Which type of regression is best for data that grows at a constant percentage rate?

--Select-- Exponential regression Linear regression Logarithmic regression

Correct! Exponential regression models data that grows or decays at a constant percentage rate.

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2. What does polynomial regression model?

--Select-- Straight lines Curves such as parabolas Constant values

Correct! Polynomial regression models curves, such as parabolas.

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