Biometry Assignment #10 ~ Simple Linear Regression (28pts)
1 - Mercury Contamination of Walleyes in IslandLake Reservoir
Goal:Develop a regression models to predict/explain mercury level found in the tissues of a walleye (ppm) using length (in.).
Data Set:Walleyes Island Lake
This assignment is similar to your simple linear regression handout; however, I want you to investigate mercury contamination levels found in walleyes (ppm)versus the length of the walleye (in.). The primary interest is in developing a walleye consumption advisory based on length for walleyes in Island Lake Reservoir near Duluth, so let Y=HGPPM and X = LGTHIN and fit a simple linear regression model.
Main Items to address:
a. Obtain a linear correlation measurement to initially investigate the linear relationship between these two variables. Are these variables linearly related to each other? Explain.
(2 pts.)
b. Perform the overall regression usefulness test (i.e. HO: Regression is not useful vs HA: Regression is useful) to formalize your initial investigation of these variables. What is your decision for this test? Write a conclusion in everyday language for this test. (2 pts.)
c. What is the RSquare value for this analysis? In the context of this problem, carefully explain what this number is measuring.(3 pts.)
d. In the context of this problem, carefully interpret the estimated y-intercept and slope of your estimated regression line.Carefully explain what these numbers are measuring. (You need to do more than say they are the y-intercept and slope of the line.) (2 pts.)
e. Discuss whether or not the assumptions for this procedure are being meet. Also, identify any outliers in the data set. (4 pts.)
Checking the assumptions:
Model Appropriate: Make sure no existing trends remain in the residual plot.
> Constant Variance: Make sure there is no megaphone patterns in the residual plot
Independence: Don’t really need to check this as these data are collected over
time.
> Normality: Make a histogram of the residuals and make sure they follow a normal
distribution
> Outliers: Any observations that fall outside ±2*RMSE are considered possible outliers.
f. It is recommended that humans should not consume more than one fish per month with mercury levels in its tissues greater than .5 ppm. Because your average walleye angler does not carry a spectrometer in their fishing boat, actually measuring the Hg level found in a walleye they have just caught is a problem. However, it is very easy for an angler to measure the length of their walleye in inches.
Using your regression, model what length of walleye would you recommend for the “do not eat more than one walleye exceeding ______inches per month” advisory? (1 pt.)
It is also recommended that humans should never consume fish with mercury levels exceeding 1 ppm in their tissues. Complete the following “we recommend that you do not eat any walleyes exceeding ______inches from IslandLake”. (1 pt.)
g. Using your regression analysis, estimate the mean mercury level found in the population of walleyes in IslandLake that are the lengths below. Give both a single value estimate and a 95% confidence interval for the mean. Also give the correct interpretation of the confidence interval for each case.
a) 21.2 inches in length (Note: this is the actual length of one of the walleyes in the data)(3 pts.)
b) 11 inches in length (Note: this is the actual length of one of the walleyes in the data) (3 pts.)
h. Suppose you just caught a whopper walleye measuring 25.9 inches from IslandLake. What do predict the mercury level would be in this particular fish? Give both a single value estimate and an interval estimate, giving the correct interpretation of the interval estimate. (Note: this is the actual length of one of the walleyes in the data.) (3 pts.)
i. Would you recommend using your model to predict the mercury level for a walleye that is 8 inches in length? How about 29 inches? Explain your reasoning. (1 pt.)
j. Would you recommend using this model to predict the mercury levels for walleyes in the Mississippi River? Explain. (1 pt.)
k. The IslandLake walleye data file also contains the weight (lbs.) for each of the fish sampled. Do you think using weight as opposed to length to establish consumption advisories is a good idea? Justify your answer. (2 pts.)
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