![]() Simply input the above numbers for \(x\). Since \(b=46\), if a student weren't to study at all, they would still (according to the regression line) receive 46 marks.Į. Since \(a=10.2\), for every extra hour increase along the \(x\)-axis, the student receives \(10.2\) more marks in the exam. This is a great question for double-checking your working - it'll be pretty obvious if you've made any serious calculation errors!ĭ. Therefore, the regression line is \(y=10.2x+46\).Ĭ. Using your calculator, you can easily find the following results, Predict the grade for a student who studies forĪ. Interpret the meaning of \(a=10.2\) and \(b=46\) in the context of the question.Į. Plot the data points and the regression line on the same graph.ĭ. Find the regression line of \(y\) on \(x\).Ĭ. ![]() The number of hours students studied and their exam results are recorded in the table below. Least squares regression line with residuals These are the residuals associated with each data point. The vertical difference between these points and the line of best fit is labelled with \(\epsilon _1\), \(\epsilon _2\), \(\epsilon _3\) and \(\epsilon _4\). Note that the line does not touch any of these points. There are so many possible factors and causes of these inaccuracies that you can assume these are entirely random. other factors effecting the dependent variable or inaccurate readings when collecting the data). There could be a number of reasons for these inaccuracies (i.e. If you've seen any bivariate data you'll know that very rarely do the data points fall exactly along a straight line, even if there is a confirmed linear 'relationship' between variables. A least squares regression line is used to predict the values of the dependent variable for a given independent variable when analysing bivariate data.
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