Then, we will need to determine the margin of error, which is the product of the critical value and the slope’s standard error. Okay, so for confidence intervals, which are sometimes referred to as prediction intervals, we will use the slope of the regression equation as our point estimate. The great thing is that we already know all the steps and procedures for finding confidence intervals and significance tests from our previous units, so this is just an extension of what we already know as outlined by Stat Trek. Once we have established the conditions have been met, we are ready to conduct a confidence interval or a hypothesis test. And Random: The data is produced from a well-designed, random sample or experiment.Equal: The variance of y is the same for all values of x.Normal: For any fixed value of x, the responses of y varies according to a normal distribution.Independent: The individual observations are independent.Linear: The relationship between x and y is linear.How does the sample regression line (estimated regression line) relate to the population regression line (true regression line)?īut, before we can jump into conducting a t-test for slope we first have to check some conditions.If we estimate a value using a least-squares regression equation, what’s the margin of error?.How do we know the strength of the linear relationship between x and y in the population?.
When we desire to answer one the following questions:
So, all we have to do is let our null hypothesis demonstrate a non-straight line relationship (i.e., slope is zero) and our alternative hypothesis asserts that there is a relationship between the explanatory and response variables.Īnd now all we have to do is test our hypothesis by carrying out a t-test for the slope and the Least Square Regression Line.īut, how do we know when to use inference for regression? Recall that a horizontal line has a slope of zero, therefore the y variable doesn’t change when x changes - thus, there is no true relationship between x and y. Jenn, Founder Calcworkshop ®, 15+ Years Experience (Licensed & Certified Teacher)Īs we know, a scatterplot helps to demonstrate the relationship between the explanatory ( dependent) variable y, and the response ( independent) variable x.Īnd when the relationship is linear we use a least squares regression line to help predict y from x.īut sometimes, we wish to draw inferences about the true regression line.
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