Hypothesis Testing for the Slope of a Least Squares Regression Line, Statistics

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Hypothesis Testing for the Slope of a Least Squares Regression Line

If the random errors of the simple linear regression are normally distributed, then the sampling distribution of b is normal.
To calculate the estimator of the standard deviation of b, s_b , the quantities of S_xx, S_xy , and S_yy will be needed.
To test the slope of the regression line β, use the t-distribution with ν = n − 2 degrees of freedom.

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Table of Contents

I. Introduction
	Basic Ideas	17:34
II. Exploring Data
	Raw Data, Dotplots, Stemplots	27:24
	Histograms, Cumulative Frequency Plots	10:21
	Summarizing Distributions, Measuring Center	16:43
	Measuring Spread: Range, IQR, Standard Deviation	18:04
	Measuring Position: Quartiles, Percentiles, Standardized Scores	16:28
	Boxplots	10:07
	Comparing Distributions of Univariate Data	24:19
	Exploring Bivariate Data: Scatterplots	13:45
	Least Squares Regression	17:32
	Exploring Categorical Data	17:00
III. Sampling and Experimentation
	Methods of Data Collection	12:04
	Planning and Conducting Surveys	13:51
	Planning and Conducting Experiments	19:32
IV. Probability
	Experiment, Outcomes, and Sample Space	14:54
	Calculating Probability	14:13
	Probability and Events	22:08
	Intersection of Events and the Multiplication Rule	19:58
	Union of Events and the Addition Rule	18:28
	Bayes' Rule	16:59
V. Discrete Random Variables and Probability Distribution
	Random Variables	7:52
	Probability Distribution of a Discrete Random Variable	15:55
	Mean and Standard Deviation of a Discrete Random Variable	17:37
	Factorials, Combinations, Permutations	15:43
	Binomial Probability Distribution	21:38
	Poisson Probability Distribution	13:40
	Geometric and Hypergeometric Probability Distributions	19:08
	Combining Independent Random Variables	20:26
VI. Continuous Random Variables and the Normal Distribution
	Continuous Probability Distribution	6:19
	Normal Distribution	6:42
	Standard Normal Distribution	13:25
	Standardizing a Normal Distribution	12:22
	Applications of the Normal Distribution	12:20
	Finding Values When the Probability is Known	12:44
VII. Sampling Distributions
	Population and Sampling Distributions	12:02
	Mean, Standard Deviation, and the Shape of the Sampling Distribution of the Sampling Mean	4:57
	Applications of the Sampling Distribution of the Sample Mean	14:50
	Mean, Standard Deviation, and the Shape of the Sampling Distribution of the Sample Proportion	3:58
	Applications of the Sampling Distribution of the Sample Proportion	10:45
VIII. Estimation of the Mean and Proportion
	Introduction to Estimation	12:52
	Estimation of a Population Mean: Standard Deviation Known	17:03
	Sample Size for Estimation of a Population Mean	10:39
	Estimation of Population Mean: Sigma Not Known	19:25
	Estimation of Population Proportion: Large Sample	17:26
	Large Sample Confidence Intervals for Difference in Population Proportion	16:16
	Confidence Intervals for a Difference in Means	27:58
	Confidence Intervals for the Slope of a Least Squares Regression Line	18:47
IX. Tests of Significance
	Introduction: Hypothesis Tests	14:09
	Large Sample Test for a Proportion	14:30
	Large Sample Test for a Difference in Two Proportions	19:14
	Test for a Mean	14:57
	Test for a Difference Between Two Means	23:13
	Chi-Square Tests: One Way and Two Way	24:33
	Hypothesis Testing for the Slope of a Least Squares Regression Line	17:48