4.5 The Sampling Distribution of the OLS Estimator.Assumption 3: Large Outliers are Unlikely.Assumption 2: Independently and Identically Distributed Data.Assumption 1: The Error Term has Conditional Mean of Zero.4.2 Estimating the Coefficients of the Linear Regression Model.3.7 Scatterplots, Sample Covariance and Sample Correlation.3.6 An Application to the Gender Gap of Earnings.3.5 Comparing Means from Different Populations.3.4 Confidence Intervals for the Population Mean.Hypothesis Testing with a Prespecified Significance Level.Calculating the p-value When the Standard Deviation is Unknown.Sample Variance, Sample Standard Deviation and Standard Error.Calculating the p-Value when the Standard Deviation is Known.3.3 Hypothesis Tests Concerning the Population Mean.Large Sample Approximations to Sampling Distributions.2.2 Random Sampling and the Distribution of Sample Averages.Probability Distributions of Continuous Random Variables.
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#Theory based hypothesis test calculator code#
These steps are performed in the code below, using the example of price and acceleration time of 2015 cars. If this value is large, it is plausible that the result we saw occurred by chance alone, and thus there is not enough evidence to say there is a relationship between the explanatory and response variables. If this proportion is small, we have evidence that our result did not occur just by chance. Observe how many of our simulations resulted in values of \(b_1\) as extreme as the one from the actual data. Randomly shuffle the values (or categories) of the explanatory variable to create a scenario where there is no systematic relationship between the explanatory and response variable.įit the model to the shuffled data, and record the value of \(b_1\). Repeat the following steps many (say 10,000) times, using a “for” loop: To test for a relationship between a response variable and a single quantitative explanatory variable, or a categorical variable with only two categories, we perform the following steps.įit the model to the actual data and record the value of the regression coefficient \(b_1\), which describes the slope of the regression line (for a quantitative variable), or the difference between groups (for a categorical variable with 2 categories).
![theory-based hypothesis test calculator theory-based hypothesis test calculator](https://miro.medium.com/max/800/0*wZe1cRSoyPdXxCKu.png)
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4.1 Performing the Simulation-Based Test for Regression Coefficient.3.3.1 Example: When the Bootstrap is Inappropriate.3.2.7 Bootstrap Distribution for Coefficients in Bears Multiple Regression Model.3.2.6 Bootstrap Distribution for Difference in Mean Mercury Level in Florida Lakes between N and S.3.2.5 Bootstrap Distribution for Mean Mercury Level in Florida Lakes.
![theory-based hypothesis test calculator theory-based hypothesis test calculator](https://www.statisticshowto.com/wp-content/uploads/2014/10/hypothesis-testing-example.jpg)
3.2.3 Standard Error Confidence Intervals.3.2.1 Visualizing the Bootstrap Distribution.3.1.6 Bootstrap for Regression Coefficients.3.1.5 Bootstrap for Difference Between Groups.3.1.4 Bootstrap for Mean, Median, St.Dev., Prop>1.3.1.3 Bootstrap for Difference in Proportion of M&M.2.5.2 Defining New Data Before predict().2.2.2 Modeling with two Explanatory Variables.2.2.1 Modeling with one Explanatory Variable.1.4.7 Stacked and Side-by-Side Bar Graphs.1.3.3 Adding a new variable with mutate().1.3.2 Converting from categorical to quantitative.1.3.1 Converting from quantitative to categorical.1.1.4 Load data already included in R package.1.1.2 Reading Data from a Directory on Your Computer.1.1.1 Read data from a local file on your computer.0.1.3 Using R on Lawrence’s Lab Computers.