Project #35992 - Statistics - Simple Linear Progression

1. An experiment is conducted to evaluate the storage conditions for fish after it has been caught. Fish were caught and either directly put into a freezer or left out for different intervals tlag (3, 6, 9, and 12 hours) before being put into the freezer. The bacterial contamination was evaluated after 7 days of storage in the freezer. For every time point, 3 fish were caught and stored accordingly. [10 points]
 Bacteria (in units) Delay time (in hours) Fish tlag=0 tlag=3 tlag=6 tlag=9 tlag=12 1 5 23 52 140 162 2 20 41 63 122 185 3 10 39 71 105 166

1. Plot and calculate the linear regression model for the relationship between time interval between catching and freezing fish (tlag) and the units of bacterial growth (note: you can use Microsoft Excel® or any other program that is able to calculate simple linear regression models. If you do, please provide the data file in addition to the answer).
2. Explain the terms slope, intercept, and linear regression model using this example.
3. Test the hypothesis that the slope of the regression model is significant different from 0 using a significance level of α = 0.05. What is the 95% confidence interval for the slope?
1. The following data set is derived from two different analytical methods analyzing the same samples. The samples contain different concentrations of acetylsalicylic acid (ASA) added to blood. The two analytical methods are chromatographic methods and only differ in the oven temperature (35 °C vs. 45 °C) while all other parameters are held constant. Each sample is analyzed 3 times. [15 points]
 Detector signal (in mV) Spiked ASA concentration (in mg/L) Method 1 (35 °C) Method 2 (45 °C) 0.25 20 18 21 25 23 28 0.5 33 31 32 41 38 39 1.0 44 48 45 91 87 95 2.0 71 75 73 136 145 139 4.0 125 119 131 181 172 175

1. Plot the two linear regression models on one set of axes. Then calculate coefficients of determination for each of the two methods (note: you can use Microsoft Excel® or any other program that is able to calculate simple linear regression models. If you do, please provide the data file in addition to the answer). Which of the methods would you prefer for the analysis of ASA samples over a concentration range of 0.25 to 4 mg/L?
2. Calculate the 95% confidence intervals for the slopes of each of the two regression models. Do these confidence intervals overlap? What conclusions can you draw from the confidence intervals?
3. Test the hypothesis that the two slopes are not significantly different from each other. In order to do so, consider that the each of the slopes is a variable that has a mean and a standard deviation – you can use a test that has been discussed in former modules to compare the two slopes with each other.

 Subject Mathematics Due By (Pacific Time) 07/25/2014 10:00 pm
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