Mini Electricity 33 Lecture Notes PDF

SPEAKER 1 Welcome back to the mini electricity 33 ps y I'm Dr Nadal Roxton And in this mean lecture we will look at significant testing of correlations and slopes and the previous many ledges. We've looked at the slopes almost specifically in what for SPEAKER 0 aggression, partial slips. Here is th...

SPEAKER 1 Welcome back to the mini electricity 33 ps y I'm Dr Nadal Roxton And in this mean lecture we will look at significant testing of correlations and slopes and the previous many ledges. We've looked at the slopes almost specifically in what for SPEAKER 0 aggression, partial slips. Here is the output from our multiple regression looking at J. R. E Q and attendance as predictors of steps example. SPEAKER 1 For months so far we just looked at the B wait which other slopes in full form and our beat a ways which of the slopes of standardised form. We've also looked at the association between our predictors and the outcome variable and the variance explained using our square. But first, what is our again in correlation Human? SPEAKER 0 That our is the correlation between two variables in regression bigger with the association between Libya, composites of all the predictive variables and the outcome? Terrible in other words, the regression equation. SPEAKER 1 Nice on the slide that I had the general form of the regression equation, and that's how this has also stayed in Footnote Be off the end of the table. The's not remind you off the predictive variables, and you SPEAKER 0 even notice that the constant is that part of the regression equation in that so bigger is simply the association SPEAKER 1 between the predictors of a group and the outcome variable. SPEAKER 0 You also see how under the sickle that the association between all the predictive variables as a group a significant appeal is less than 0.0 so we can see that the overall regression model is significant. SPEAKER 1 You may have noticed that in the coefficients table that there are three more significance values. The top one is for the constant which were up of this is meaningless, so we'll just ignore that. The next. To show the association between Jeremy Q and sets exam SPEAKER 0 performance, while controlling for attendance is significant at 0.0 point 011 And the association between attendance assesses and performance while SPEAKER 1 controlling the Geo is significant at 0.3 What this means is that after we account for the correlation between Rick and attendance, the association between each predictor and the outcome SPEAKER 0 is significant. This will not always be the case. No one will notice in a future mini lecture. But what do we mean when we say we're testing our and by extension, the bi ways for significance in order to see what we mean by significant testing in SPEAKER 1 regression. It's easy to look at the significance in correlations. SPEAKER 0 Recall that our describes the linear relationship between two variables SPEAKER 1 and a sample. But usually we want to make inferences about the relationship in a population we asked ourselves that are large enough SPEAKER 0 to conclude that there is a linear relationship between the variables of the population or is the correlation that we find in our sample simply due to set the error? Just like expert was the man of the sample and meeting you was the meat of the population are the SPEAKER 1 correlation in the sample and wrote The little peace. SPEAKER 0 Little peace symbol is the correlation of the population. SPEAKER 1 As you lend a wonder by three p s wife, we can set up a null in alternative by processes SPEAKER 0 The correlation the null hypothesis states that row equals zero. In other words, that there is no relationship between excellent SPEAKER 1 population. SPEAKER 0 The alternate hypothesis states that row is not zero in other words, that there is a linear relationship between ex SPEAKER 1 wife in the population. We test this in a similar fashion is testing a SPEAKER 0 means testing whether Amina sample comes from a population a SPEAKER 1 specified under the null hypothesis recalled from the satellite distribution. Three cuts early in the trimester. We do the same thing here only instead of looking SPEAKER 0 at me, we look att, correlation coefficients. SPEAKER 1 We take a random sample and calculate the correlation. SPEAKER 0 We then do this repeatedly for an infinite number of SPEAKER 1 samples. We then fine, just like just like you would with SPEAKER 0 a random sample of needs. There's a correlation in our various examples. Do not always equal zero the value. The coronation will vary from one rant example toe another. SPEAKER 1 As a result, we cannot be certain that the correlation SPEAKER 0 we get from a sample reflect what the correlation would be in the population, and particularly whether it comes from SPEAKER 1 a population which the coronation is zero. SPEAKER 0 It may be that the correlation has come from a SPEAKER 1 population in which the true value off the correlation is SPEAKER 0 lessons or greater than zero. SPEAKER 1 Therefore, we use our understanding of sample distribution to calculate SPEAKER 0 a probability or a likelihood that the sample was taken for our population, where the correlation is zero. SPEAKER 1 Fortunately for us, when correlation in the in the population zero When the null hypothesis is true for a large enough sample, I will be NAMI distributed around Syria. So we asked ourselves, Is our sample coronation significantly greater SPEAKER 0 or significant? Less than zero? And then now we can address the question as to whether our is large enough to conclude that there is SPEAKER 1 a non zero correlation in the population, or whether that SPEAKER 0 correlation in the sample simply is just due to sample era. We use our probability or a P value of 0.5 to reject them now hypothesis. SPEAKER 1 Just like we do for T tests and tests and so on. Large correlations will be more likely to reject the mouth hypothesis in indicated. SPEAKER 0 There actually is a relationship between the variables in the SPEAKER 1 population. In the online materials, there's a screen cast demonstrating this concept. In the screen cast, we use a population of scores SPEAKER 0 of headless nick, the correlation between Hellickson IQ zero on SPEAKER 1 the population. In the demonstration, I draw several random samples from this population with a nine correlating the population of zero, and you'll see that some of the samples find a significant positive association. Others find a significant negative association and others find no association. This demonstrates that sometimes you'll find correlations and samples that indicate significant association between two variables, even when there's actually no correlated in the population. SPEAKER 0 Now what we just looked at correlations. We do exactly the same thing for the weights. A small point to note is that in coronations that are refers to the correlation sample and road refers to the correlation of population in regression. The letter B refers to the sample B wait and in some text beater is also used to refer to be within the population. This is not a particular issue for this course, but just a heads up. In case you see, Beata used Teo, give you an estimate off the B wait in the population. SPEAKER 1 So let's return to our GR eek exam. SPEAKER 0 Here is the buy very regression from earlier in the Tri Nesa were just Jari Hewas predict Ross. SPEAKER 1 That's exam performance. Here we consider the bee way to 0.6 eight is SPEAKER 0 significant as 0.9 is less than our critical cut off point 0.5 more fully, we would say that the bee weight of GR Hugh is significantly different from Syria. That is, the weight of 0.68 would occur by chance and the populations Truby weight of zero less than 5% SPEAKER 1 of the time. SPEAKER 0 Like White looking at the buy verite regression off attendants, we again find a significant association, which that's example, for SPEAKER 1 months. SPEAKER 0 And finally, with both predictors in the regression, we can SPEAKER 1 see that both are significant predictors of stats, exam performance even were controlling for the coronation between the two predictors. Again, I'm not that this will not always be the SPEAKER 0 case. SPEAKER 1 Sometimes you will have significant correlations that significant associations between SPEAKER 0 the predict the variable and an outcome variable in there by their aggression. SPEAKER 1 But the association becomes not significant when you added other SPEAKER 0 predictors to summarise just with that other analysis, like the teat. If we checked the significance of it over our B wait the correlation of the population's refer to as robe. SPEAKER 1 We use the same concept off sampling distributions as we SPEAKER 0 use with me the test, whether the correlation or the be waiting a sample is significantly different from Ciro. SPEAKER 1 In addition to testing whether there's a significant association between SPEAKER 0 our predictors as a group. SPEAKER 1 In other words, and then your combination for the regression SPEAKER 0 equation by looking at bigger. We also test the significance of each predictor for controller, SPEAKER 1 for all our predictors, by looking at the significance of SPEAKER 0 the B wait.