# Hypothesis Testing and Scatter Plots

I need help (step-by-step) with the following questions for my upcoming test. (please see attached). Please explain the process of figuring these questions out. I have an upcoming final and I need to know how to do these problems.

A random sample of eight quarterback listed in The Sports Encyclopedia: Pro Football, gave the following information.

Let x = height of a quarterback in inches, and let y = weight of a quarterback in pounds.

x 75 78 74 73 72 75 76 73

y 205 230 210 210 195 215 203 196

a) Draw a scatter plot.

b) Calculate the correlation coefficient

c) Make a conclusion based upon the correlation coefficient.

d) Calculate the equation of the regression line and draw the line in your scatter plot.

e) If a quarterback is x = 76 inches tall, what can you predict is the weight of this quarterback?

f) Calculate the coefficient of determination.

g) Interpret the coefficient of determination in terms of your data.

h) Calculate the stand error of the estimate.

i) Interpret the standard error of the estimate in terms of your data.

j) Construct a 95% prediction interval for the weight of the quarterback when the height is 70 inches and interpret the results.

#### Solution Preview

a) See attached

b) See attached

c) Make a conclusion based upon the correlation coefficient.

Since the correlation coefficient is positive, there is a positive relationship exists between the height and weight of quarterback. Since the correlation coefficient is close to 1, there is a strong relationship exists between the variables. Thus there is a strong positive linear relationship exists between the height and weight of quarterback.

d) Calculate the equation of the regression line and draw the line in your scatter plot.

The general form of simple linear regression is Y= a + bX

Where Y is the dependent variable and X is the independent variable, a and be are known as the regression coefficients .They are estimated by ...

#### Solution Summary

Hypothesis testing and scatter plots are examined.