Simple Linear Regressions

this is going to be the lecture on how to perform a simple linear regression uses the same data set that was in the correlation video essentially we have a participant ID people's levels of social anxiety rejection sensitivity depressive symptoms and disgust sensitivity these are all measured on one to seven scales where higher numbers indicate more of whatever their personality construct is so more social anxiety more sensitive to rejection more depressive symptoms more disgust so we use linear regression simple linear regressions when we have one independent variable and we want to see if it successfully predicts another outcome variable a dependent variable so the way we'll do this is we'll go to analyze regression linear there are lots of kinds of regressions this is just for the simple linear regression we'll see we have dependent box in an independent box we're going to take R in this case let's see what predicts depressive symptoms and we'll put that in the dependent and then let's take rejection sensitivity and put that in the independent this would be testing to see if one's rejection sensitivity predicts depressive symptoms all we're going to do next is hit OK now we're going to have a bunch of windows that appear bunch of boxes the first box lets us know what variables are being used to predict what variable in this case we can see that level of rejection sensitivity is being used to predict the dependent variable amount of depressive symptoms we get next go to our model summary and our ANOVA table the first thing we should probably look at is the ANOVA table the ANOVA table lets us know if our model is a significant model if the model isn't significant nothing else matters what it means for a model to be significant is are the predictor variables in this case only one variable rejection sensitivity a good predictor are they good predictors of the outcome variable in this case depression depressive symptoms we determine that by looking at the against value of our model in this case our significance value is 0.029 this is less than alpha point zero five therefore the model is significant we would report the model significance as f parentheses 1 comma 16 our degrees of freedom equals five point seven five nine our F value comma P equals point zero two nine which is our p value our significance value we can go back up to our model summary we can look at our R square in fact we're going to actually look at our adjusted r-square if you multiply the adjusted r-square by a hundred and interpret this as a percentage this gives you the percentage of the variance in the dependent variable explained by the independent variable in this case we would say that twenty one point nine percent of all of the variability in depressive symptoms can be explained by one's level of rejection sensitivity if we go down to the very bottom box these are our regression coefficients if your goal is to write the equation for the line that uses rejection sensitivity to predict depressive symptoms we're going to look at our unstandardized coefficients the point three zero six is the slope the beta the slope for level of rejection sensitivity the number one point one zero eight that is in the constant line that is the y-intercept which means that the equation of the line for using rejection sensitivity to predict depressive symptoms would be y predicts equals point three zero six x plus one point one zero eight to determine whether or not the level of rejection sensitivity that slope is significant we go over to the significance value and see that it is significant that t-test comparing that slope to a slope of zero is T 2.4 with a significance value of point zero to nine we can try another predictor we can go back to regression linear instead of depressive symptoms let's use disgust sensitivity to predict depressive symptoms if we hit okay we again see now that were discussed sensitivity is predicting depressive symptoms we go down to our model and our ANOVA table the ANOVA is not significant it looks like disgust does not successfully predict depressive symptoms in fact it does a terrible job of predicting almost none less than none of the variance is predicting and we can again see that the slope is very very small very close to zero it's not different from zero in this case disgust sensitivity is a bad predictor of depressive symptoms that concludes the discussion on simple linear regressions

Channel: bernstmj

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Keywords: Statistics, Psychology, Academia, Math

Id: vnQIW5ts3eM

Length: 5min 32sec (332 seconds)

Published: Tue Jun 21 2011