Correlation and Regression



Core Maths assessmentSheet MERGEFIELD Sheet 1Correlation and RegressionQ1)The table below shows the heights and foot lengths of 12 girls.Height(cm)156175173146159167147148171168176160Foot length (cm)19242723242518242722 MERGEFIELD Q1FL11 22 MERGEFIELD Q1FL12 21a)i) Find the mean height h and the mean foot length f for the 12 girls(2 marks)ii)Calculate the correlation coefficient between f and h.(1 mark)ii)Calculate the equation of the line of best fit of f on h(2 marks)b) Briefly describe the gradient of the line in terms of foot length and the height of girls.(2 marks)The correlation coefficient between the heights and foot lengths for boys is MERGEFIELD Q1_Male_PMCC 0.7374. Comment on what this tells us in comparison to the data for girls.(2 marks)(TOTAL 9 marks)Continued on next pageQ2) As part of an experiment, a person was asked to hold a 100g weight in one hand while holding another object in their other hand.They were asked to estimate the weight of the object and the results are shown below.Actual weight(grams)Estimated weight(grams)18153420 MERGEFIELD Q2Act1 46 MERGEFIELD Q2Es1 3060407545 MERGEFIELD Q2Act2 93 MERGEFIELD Q2Es2 55134100201120With reference to the value of r (given to 3dp), describe the correlation between the actual weight, (x) and the estimated weight (y).(3 marks)The equation of the regression line is given by y= MERGEFIELD Q2_a 1.9203 + MERGEFIELD Q2_b 0.6197xExplain why this equation is not appropriate when x=0(1 mark)Use the regression equation to predict the estimated weight of an object that is actually MERGEFIELD Q2_input 119 grams (1 mark)Would you expect your answer to bii) to be reliable? Explain your reasons.(2 marks)(TOTAL 7 marks) ................
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