![calculate the linear regression equation T TEST calculate the linear regression equation T TEST](https://mathcracker.com/images/legacy/Mpl_example_scatter_plot.png)
Together we will use the slope and y-intercept of the least-squares regression to estimate the slope and y-intercept of the population regression line, construct confidence intervals, and use a significance tests for the slope to determine the linear relationship between x and y in the population. And as always, we will ensure that we can calculate the necessary values by hand and with technology. I understand where Students t-distribution comes from, namely I can. We will work through how to calculate the confidence interval and draw inferences about the true regression line by using raw data as well as summary statistics and computer output data. I know how to calculate t-statistics and p-values for linear regression, but Im trying to understand a step in the derivation. The standard error of the slope is calculated by dividing the standard deviation of the residuals by the square root of the sum of the squares for x. The critical value, or t-interval, is found using a t-distribution with n-2 degrees of freedom. 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.
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Linear refers to the fact that we use a line to fit our data. Independent: The individual observations are independent. Linear Regression models have a relationship between dependent and independent variables by fitting a linear equation to the observed data.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: The two test statistic formulas are algebraically equal however, the formulas are different and we use a different parameter in the hypotheses. 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? In the STAT list editor, enter the (X) data in list L1 and the Y data in list L2, paired so that the corresponding ((x,y)) values are next to each other in the lists. Using the Linear Regression T Test: LinRegTTest. The y y is read y hat and is the estimated value of y. USING THE TI-83, 83+, 84, 84+ CALCULATOR. 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. Each point of data is of the the form ( x, y) and each point of the line of best fit using least-squares linear regression has the form (xy) ( x y ). For Mark: it does not matter which symbol you highlight.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.For TYPE: highlight the very first icon which is the scatterplot and press ENTER.On the input screen for PLOT 1, highlight On, and press ENTER.We are assuming your \(X\) data is already entered in list L1 and your \(Y\) data is in list L2.Graphing the Scatterplot and Regression Line
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For now, just note where to find these values we will discuss them in the next two sections.