resolve all 3 please

Question 1 Conor uses a 3D printer to produce various pieces for a model. He records the time taken, t hours, to produce each piece, and its base area, x cm2. Base area, x (cm-) 1.1 1.3 1.9 2.2 2.5 3.7 Time, t (hours) 0.7 0.9 1.5 1.8 2.2 3.8 a Calculate the product moment correlation coefficient between log x and log t. (2 marks) b Use your answer to part a to explain why an equation of the form ? = ax", where a and n are constants, is likely to be a good model for the relationship between x and t. (1 mark) c The regression line of log t on log x is given as log = -0.210 + 1.38 log x. Determine the values of the constants a and n in the equation given in part b. (2 marks) Question 2 The following table shows the engine size (c), in cubic centimetres, and the fuel consumption (f), in miles per gallon to the nearest mile, for 10 car models. c (cm3) 1000 1200 1400 1500 1600 1800 2000 2200 2500 3000 f (mpg) 46 42 43 39 41 37 35 29 28 25 a Use your calculator to find the value of the product moment correlation coefficient between c and f. (1 mark) b Interpret your answer to part a. (2 marks) Question 3 As part of a survey in a particular profession, age, x years, and yearly salary, fy thousands, were recorded. The values of x and y for a randomly selected sample of ten members of the profession are as follows: x 30 52 38 48 56 44 41 25 32 27 22 38 40 34 35 32 28 27 29 41 a Calculate, to 3 decimal places, the product moment correlation coefficient between age and salary. (1 mark) It is suggested that there is no correlation between age and salary. b Test this suggestion at the 5% significance level, stating your null and alternative hypotheses clearly.