Question: Regression Problem

Taltson Lake is in the Canadian Northwest Territories. This lake has many Northern Pike. The following data was obtained by two fishermen visiting the lake. Let x = length of a Northern Pike in inches and let y = weight in pounds.

1. Draw a scatter diagram. Using the scatter diagram (no calculations) would you estimate the linear correlation coefficient to be positive, close to zero, or negative? Explain your answer.
2. For the given data compute each of the following.

1. \(\bar{x}\) and \(\bar{v}\)
2. \(\Sigma x, \Sigma y, \Sigma x^{2}, \Sigma y^{2}, \Sigma x y\)
3. The slope \(b\) and \(y\) intercept \(a\) of the least squares line; write out the equation for the least squares line.
4. Graph the least squares line on your scatter plot of problem 1

iii. Compute the sample correlation coefficient \(r\). Compute the coefficient of determination. Give a brief explanation of the meaning of the coefficient of determination in the context of this problem.

iv. Compute the standard error of estimate \(\mathrm{Se}\).

v. If a 32 inch Northern Pike is caught, what is the weight in pounds as predicted by the least squares line?

vi. Find a \(90 \%\) confidence interval for your prediction of Problem 5 .

vii. Using the sample correlation coefficient \(r\) computed in Problem 3, test whether or not the population correlation coefficient \(\rho\) is different from zero. Use \(\alpha=0.01\). Is \(r\) significant in this problem? Explain.

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