for c) e) f) g) questions please solve the problems "by hand" (you may do partial calculations in R though)

show detailed works and steps, if use R for a) and b)

c) d) e) f) g) please don't just give me an R output Please provide detailed steps how you get the answers,

?

1. Consider 10 pairs of data relating shoe length and height: Shoe Length (x) 9 10 10.5 11 11.5 11.75 12 12.5 12.75 13 Height (y) 62 64 64.5 69 70 73 72 75 74 77 (a) Create a scatter plot of the shoe length versus height data (you may use R to do this). Does the plot suggest a strong linear relationship? (b) Fit the model Y = Bo + Bir + e. Plot the linear regression line as well. (c) Calculate the correlation coefficient for this data. (d) Test Ho : p = 0 versus Hi : p # 0 at a significance level of a = 0.05. (e) Suppose a crime scene investigator finds a shoe print that measures 11.25 in long and would like to estimate the height of the person who made the print. Based on the regression equation you found, what is the "best predicted" height of the person who made the print? (f) Find a 95% confidence interval for the mean value of height mea- surements for a person for which the shoe length is 11.25 in long. (g) Find a 95% prediction interval for the height for a person for which the shoe length is 11.25 in long. Compare the length of this interval to that of (f) and comment on your finding