1.Show a vector X of integers from 31 to 45. Generate

a.the summary table for X;

b.a histogram for X.

2.Now read vector X into a 53 matrix A (read the entries in such that 31, 32, and 33 are the entries in the first row). Show a 23 matrix of ones, and append it to A below. Call the new matrix B.

a.Compute the column means of B.

3.The CVS file Men 100 M. CVS contains the race times of all the medalists in the Men's 100 M race. Read this in as a data frame. Make sure that Time is a numerical variable, and Medal is a factor variable.

a.Generate the summary table for race times.

b.Show a box plot for race times broken up by Medal (G, S, and B).

c.Show a table of average running times broken up by Medal.

d.Show a new logical variable in the data frame called Sub 10 defined to be TRUE if the running time was less than 10 seconds, and FALSE if time was greater than or equal to 10 seconds.

e.Show a numerical variable Sub 10 N defined to be 1 if Sub 10 is TRUE and 0 if FALSE.

4.Create two cross tabulations where rows are the country of the runner and columns are medal (G, S, and B). The entries should be:

a.Average running time

b.Number of medals

5.What is the average time of all US gold medalists? How many Jamaican silver medalists have there been?

6.Show a scatter plot with year of the games on the X-axis and medal times on the Y-axis. Use different colors or symbols to distinguish between gold, silver and bronze medal times.

7.Run a linear regression with gold medal times as the dependent variable and year of the games as the independent variable.

a.What would be the predicted gold medal time for the 2024 games?

b.Would a quadratic model explain more of the variation in running times? Explain.

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