no copy and paste

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 (t_lag = 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 (t_lag) 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 = 0.05. What is the 95% confidence interval for the slope?

NOTE: for part a only, 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. Be careful using Excel or other programs for part c as we are asking you to compare the slope to 0, and the regression packs in such programs often calculate a different variable. This could result is significant point deductions and it is therefore recommended to perform the calculations for part c outside of the regression package.

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.
2. Which of the methods would you prefer for the analysis of ASA samples over a concentration range of 0.25 to 4 mg/L?
3. Calculate the 95% confidence intervals for the slopes of each of the two regression models. Do these confidence intervals overlap? What information can you draw from the confidence intervals?
4. 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.

NOTE: for part a only, 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. Be careful using Excel or other programs for parts c and d as we are asking you to compare the slope to each other, and the regression packs in such programs often calculate different variables. This could result is significant point deductions and it is therefore recommended to perform the calculations for parts c and d outside of the regression package.