Data set attached

Q1. [23 marks] Trying to avoid over- or under-allocating labour hours in a particular moving job, the owner of a moving company would like to develop a better method of predicting labour hours (Duration; measured in hours) by using the size of the apartment (Size; measured in cubic feet) moved. A random sample of 36 moves in the past year was randomly selected in the borough of Manhattan in New York City. The data set "S1 124 HW2 Q1 Data.xIsx" second page. a) Use R Studio to produce a scatter plot, without the least square regression line. Customize the plotting symbol and colour. Add proper labels to both x-axis and y-axis. Add a title. Attach the R codes and the scatter plot. b) Provide a description of the scatter plot in a). c) Use R Studio to compute the correlation coefficient. Attach the R codes and output. d) Can we conclude that there is a significant correlation between the moving hour and size of all apartments? Make sure you use the three-step process and an appropriate decision point to answer this question. I e) Use R Studio to conduct regression analysis, attach the output. f) Use R Studio to produce a scatter plot, with the least square regression line. Attach the R code and scatter plot. g) Write out the least square regression line. h) Provide an interpretation of the intercept estimate and the slope estimate. [2+2] Note: the interpretation may not make sense, but do it regardless, for the sake of practice. i) Check all three assumptions. In other words, make sure you provide the correct graph and comment about the validity of the assumptions. j) How much labour time is needed when the moving unit is 956 cubic feet? Provide your answer with 95% confidence level.