4. The following table lists the weights and heights of five boys: Boys Sam Tom Peter Mike Jack Weights (lb.) 120 125 125 135 145 Heights (in.) 61 60 64 68 72 a) Find the covariance matrix for the data. b) Make a principal component analysis of the data to find a single size index that explains most of the variation in the data.

The top portion of the Pearson's r correlation coefficient equation calculates the______ whereas the bottom portion calculates the___ 1)variance of x and the variance of y; covariance between variables x and y 2)covariance of variable ×; covariance of variable y 3)covariance between variables x and y; variance of x and the variance of y 4)covariance of variable v: covariance of variable x.

Data: 3.5, 3.2, 3.1, 3.5, 3.6, 3.2, 3.4, 2.9, 4.1, 2.6, 3.3, 3.5, 3.9, 3.8, 3.7, 3.4, 3.6, 3.5, 3.5, 3.7, 3.6, 3.8, 3.2, 3.4, 4.2, 3.6, 3.1, 2.9, 2.5, 3.5, 3.1, 3.2, 3.7, 3.8, 3.4, 3.6, 3.5, 3.2, 3.6, 3.8 Sketch a histogram with ranges of 0.1, from minimum (2.5) to maximum (4.2) values. Then sketch a histogram with ranges of 0.3. You can include the relative frequency scales on the same sketches.

1.) The data in the table below show years of teaching experience and annual salary in dollars for 12 randomly selected mathematics instructors in Illinois colleges/ universities for the 2013/2014 school year. Is there a linear correlation between a mathematics instructor’s years of experience and his or her annual salary?  Number of Years 7 9 6 7 11 12 11 3 3 7 9 1 Salary (in Dollars) $48,897.00 $62,866.00 $54,585.00 $56,611.00 $53,541.00 $53,541.00 $47,027.00 $47,970.00 $46,668.00 $48,029.00 $46,735.00 $45,000.00  THE OTHER QUESTION 2.) Does incubation or gestation time affect an animal’s average lifespan? Some animals have lifespans that average well over 100 years. The following table lists animals that have some of the longest lifespans on the earth. Is there a correlation between an animal’s gestation/incubation period and its average lifespan in years?  Animal: Nile crocodile, Aldabra giant tortoise, Lake sturgeon, Galápagos tortoise, Bowhead whale Average Lifespan (in…