Data below show the height (in cm) )of a group of 10 children aged 3 to 12 years He: ht 1030 1098 1164 122.4 128.2 1338 139.8 1450 1505 ()cm Age 3 4 5 7 1 0 1 1 12 (years) The equation of the least squares regression line for this set of data is: height = 6.036 X age + 79.147 a) Interpret the value 79.147 in terms of the variables. Briefly explain if this is reasonable. [2 marks] b) State the slope of the regression line. What does the slope suggest in terms of the variables involved? [2 marks] c) Use the regression line to predict the height of a 15-year-old child. Is this an example of interpolation or extrapolation? [2 marks] d) Comment on the reliability of your prediction in part c). [1 mark] e) The residual plot for this analysis is shown below. 25 Res-due i: m O ,_ m 9 Briefly explain why this residual plot suggests that a linear equation is not the most appropriate model for this relationship. ['I mark] f) Apply the square transformation (height)2 to transform the data. Give the equation of the transformed regression in the form (height)2 = a X age + b, with coefficients rounded to 2 decimal places. [2 marks] 9) Use the transformed equation from part f) to predict the height of an 8 year-old girl. Comment on whether this prediction is reliable or not, clearly explaining your answer. [2 marks]