4.2. Suppose that we are interested in testing whether horsepower (HP) and / or the weight of a vehicle have a high influence in the consumption of petrol, i.e. litres per kilometre (Ipkm). Hence, suppose that 20 different vehicles are tested and the following is observed: Ipkm HP Weight 44 67 1844 44 50 1998 40 62 1752 37 69 1980 37 66 1797 34 63 2199 35 90 2404 32 99 2611 30 63 3236 28 91 2606 26 94 2580 26 88 2507 25 124 2922 22 97 2434 20 114 3248 21 102 2812 18 114 3382 18 142 3197 16 153 4380 16 139 4036Question 4: Regression Models [25] 4.1. Consider the following sample of 10 class test 1 (CT1) and semester test 1 (ST1) marks for Statistical Inference class: CTI 100 83 71 55 75 98 65 85 65 95 STI 99 88 93 50 87 99 81 94 57 89 4.1.1 Using first principle, develop a regression equation that would help the lecturer predict the ST1 marks of a student using CT1 marks. (Use MS Excel and show all calculations / steps) (5) 4.1.2 Predict a ST1 mark for a student who obtained a 59 for CT1. (1) 4.1.3 Use MS Excel to develop a regression model - include the Summary Output in your answer. (4) 4.1.4 Based on the output in 4.1.3, comment / interpret the following metric with relevance to the analyzed dataset based on student's marks: (3) R square Significance of the F-test (i.e. relationship between CT1 & ST1 marks) eee Are the coefficients of the regression model the same as those in 4.1.1? (See next page for Question 4.2)