Name: Multiple Regression
Uploaded: 2022-12-05T11:21:50-05:00
Duration: 1 min 25 s
Description: Multiple regression assesses a linear relationship between one response or dependent variable and two or more independent variables.

Chapter 11: Correlation and Regression Back To Chapter

11.10: Multiple Regression

TABLE OF
CONTENTS

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Chapter 1: Understanding Statistics

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1.1: Introduction to Statistics
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1.2: How Data are Classified: Categorical Data
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1.3: How Data are Classified: Numerical Data
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1.4: Nominal Level of Measurement
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1.5: Ordinal Level of Measurement
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1.6: Interval Level of Measurement
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1.7: Ratio Level of Measurement
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1.8: Data Collection by Observations
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1.9: Data Collection by Experiments
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1.10: Data Collection by Survey
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1.11: Random Sampling Method
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1.12: Systematic Sampling Method
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1.13: Convenience Sampling Method
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1.14: Stratified Sampling Method
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1.15: Cluster Sampling Method

Chapter 2: Summarizing and Visualizing Data

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2.1: Review and Preview
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2.2: What is a Frequency Distribution
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2.3: Construction of Frequency Distribution
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2.4: Relative Frequency Distribution
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2.5: Percentage Frequency Distribution
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2.6: Cumulative Frequency Distribution
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2.7: Ogive Graph
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2.8: Histogram
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2.9: Relative Frequency Histogram
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2.10: Scatter Plot
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2.11: Time-Series Graph
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2.12: Bar Graph
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2.13: Multiple Bar Graph
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2.14: Pareto Chart
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2.15: Pie Chart

Chapter 3: Measure of Central Tendency

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3.1: What is Central Tendency?
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3.2: Arithmetic Mean
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3.3: Geometric Mean
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3.4: Harmonic Mean
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3.5: Trimmed Mean
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3.6: Weighted Mean
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3.7: Root Mean Square
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3.8: Mean From a Frequency Distribution
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3.9: What is a Mode?
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3.10: Median
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3.11: Midrange
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3.12: Skewness
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3.13: Types of Skewness

Chapter 4: Measures of Variation

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4.1: What is Variation?
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4.2: Range
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4.3: Standard Deviation
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4.4: Standard Error of the Mean
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4.5: Calculating Standard Deviation
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4.6: Variance
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4.7: Coefficient of Variation
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4.8: Range Rule of Thumb to Interpret Standard Deviation
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4.9: Empirical Method to Interpret Standard Deviation
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4.10: Chebyshev's Theorem to Interpret Standard Deviation
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4.11: Mean Absolute Deviation

Chapter 5: Measures of Relative Standing

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5.1: Review and Preview
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5.2: Introduction to z Scores
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5.3: z Scores and Unusual Values
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5.4: Percentile
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5.5: Quartile
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5.6: 5-Number Summary
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5.7: Boxplot
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5.8: What Are Outliers?
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5.9: Modified Boxplots

Chapter 6: Probability Distributions

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6.1: Probability in Statistics
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6.2: Random Variables
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6.3: Probability Distributions
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6.4: Probability Histograms
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6.5: Unusual Results
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6.6: Expected Value
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6.7: Binomial Probability Distribution
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6.8: Poisson Probability Distribution
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6.9: Uniform Distribution
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6.10: Normal Distribution
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6.11: z Scores and Area Under the Curve
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6.12: Applications of Normal Distribution
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6.13: Sampling Distribution
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6.14: Central Limit Theorem

Chapter 7: Estimates

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7.1: What are Estimates?
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7.2: Sample Proportion and Population Proportion
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7.3: Confidence Intervals
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7.4: Confidence Coefficient
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7.5: Interpretation of Confidence Intervals
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7.6: Critical Values
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7.7: Margin of Error
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7.8: Sample Size Calculation
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7.9: Estimating Population Mean with Known Standard Deviation
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7.10: Estimating Population Mean with Unknown Standard Deviation
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7.11: Confidence Interval for Estimating Population Mean

Chapter 8: Distributions

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8.1: Distributions to Estimate Population Parameter
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8.2: Degrees of Freedom
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8.3: Student t Distribution
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8.4: Choosing Between z and t Distribution
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8.5: Chi-square Distribution
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8.6: Finding Critical Values for Chi-Square
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8.7: Estimating Population Standard Deviation
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8.8: Goodness-of-Fit Test
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8.9: Expected Frequencies in Goodness-of-Fit Tests
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8.10: Contingency Table
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8.11: Introduction to Test of Independence
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8.12: Hypothesis Test for Test of Independence
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8.13: Determination of Expected Frequency
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8.14: Test for Homogeneity
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8.15: F Distribution

Chapter 9: Hypothesis Testing

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9.1: What is a Hypothesis?
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9.2: Null and Alternative Hypotheses
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9.3: Critical Region, Critical Values and Significance Level
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9.4: P-value
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9.5: Types of Hypothesis Testing
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9.6: Decision Making: P-value Method
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9.7: Decision Making: Traditional Method
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9.8: Hypothesis: Accept or Fail to Reject?
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9.9: Errors In Hypothesis Tests
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9.10: Testing a Claim about Population Proportion
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9.11: Testing a Claim about Mean: Known Population SD
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9.12: Testing a Claim about Mean: Unknown Population SD
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9.13: Testing a Claim about Standard Deviation

Chapter 10: Analysis of Variance

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10.1: What is an ANOVA?
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10.2: One-Way ANOVA
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10.3: One-Way ANOVA: Equal Sample Sizes
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10.4: One-Way ANOVA: Unequal Sample Sizes
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10.5: Multiple Comparison Tests
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10.6: Bonferroni Test
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10.7: Two-Way ANOVA

Chapter 11: Correlation and Regression

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11.1: Correlation
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11.2: Coefficient of Correlation
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11.3: Calculating and Interpreting the Linear Correlation Coefficient
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11.4: Regression Analysis
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11.5: Outliers and Influential Points
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11.6: Residuals and Least-Squares Property
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11.7: Residual Plots
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11.8: Variation
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11.9: Prediction Intervals
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11.10: Multiple Regression

Chapter 12: Statistics in Practice

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12.1: What is an Experiment?
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12.2: Study Design in Statistics
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12.3: Observational Studies
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12.4: Experimental Designs
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12.5: Randomized Experiments
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12.6: Crossover Experiments
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12.7: Controls in Experiments
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12.8: Bias
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12.9: Blinding
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12.10: Clinical Trials

Full Table of Contents

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Multiple Regression

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11.9: Prediction Intervals

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TRANSCRIPT

Multiple regression is a statistical tool used to analyze the relationship between more than two variables.

Multiple regression can be modeled into a simple equation that estimates the linear relationship between the response or dependent variable, with more than one predictor or independent variables.

For example, the water consumption of athletes is positively correlated with both the temperature and the total amount of time practiced.

Here, the temperature and the total amount of time practiced are the predictor variables that can be independently set. The water consumption is the response variable as it depends on the other two variables.

Since the manual calculation of the multiple regression equation is generally complex, software is used to solve it.

The multiple coefficient of determination is calculated to measure how well the equation fits the data set. It means that the changes in temperature and the total amount of time practiced can explain 97% of the variation in water consumption.

However, as more variables are used, R² generally increases.

In such cases, the adjusted coefficient of determination is calculated, which accounts for the sample size and the number of predictor variables.

11.10: Multiple Regression

Multiple regression assesses a linear relationship between one response or dependent variable and two or more independent variables. It has many practical applications.

Farmers can use multiple regression to determine the crop yield based on more than one factor, such as water availability, fertilizer, soil properties, etc. Here, the crop yield is the response or dependent variable as it depends on the other independent variables. The analysis requires the construction of a scatter plot followed by a multiple linear regression equation to calculate the multiple coefficient of determination, R². Suppose the value of R² is 96%; one can interpret that the different combinations of water and fertilizer explain 96% of the variation in the crop yield.

However, the value of R² increases with the number of independent variables. So, an adjusted coefficient of determination that accounts for both - the sample size and number of variables is used during analysis.

Chapter 1: Understanding Statistics

Chapter 2: Summarizing and Visualizing Data

Chapter 3: Measure of Central Tendency

Chapter 4: Measures of Variation

Chapter 5: Measures of Relative Standing

Chapter 6: Probability Distributions

Chapter 7: Estimates

Chapter 8: Distributions

Chapter 9: Hypothesis Testing

Chapter 10: Analysis of Variance

Chapter 11: Correlation and Regression

Chapter 12: Statistics in Practice

11.10: Multiple Regression

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