The data for this exercise includes measurements of bacteria counts following th

Question

The data for this exercise includes measurements of bacteria counts following the culturing of a strains of Staphylococcus aureus. We wish to understand what combination of experimental factors produce the greatest counts of bacteria. The primary factors of interest are the time and the temperature used. We will also want to control for the concentration levels. For these analyses the data is set up with dummy variables where TIME = 0 if time was 24 hours TIME = 1 if time was 48 hours TEMP = 0 if temp was 27 TEMP = 1 if temp was 35 CONC is a continuous measure of the solution concentration. COUNT is the dependent outcome of the count of bacteria present. We will treat this as a continuous variable in these analyses. For each of the following you can use the online program at http://www.wessa.net/rwasp multipleregression.wasp (see class examples for using this program.) Run a multiple linear regression model predicting COUNT ("endogenous" variable) with TEMP, TIME, and CONC as predictors in the model. What is the estimated difference in counts between the two experimental times (based on model coefficient) and in counts between the two temperatures? Based on this model, what combination of time and temperature (time = 24 and temp = 27, time = 24 and temp = 35, time = 48 and temp = 27, or time = 48 and temp = 35) will yield the highest count? Add a fifth column to the data which is set to 1 if temp = 1 and time = 1 and otherwise is set to 0. This is the interaction term for time and temperature. Rerun the above including this interaction term. What is the p-value for testing the interaction? What does this suggest about temperature and time and bacteria counts? Based on this model what combination of time and temperature yields the highest count?

Explanation / Answer

1. By running multiple linear regression model (i have done it in excel)

I got y = - 68.65 + 110.5x + 71.7t + 89.1h + error

where y = count , x = conc , t = time [ 0 for 24 hours and 1 for 48 hours] and h = [ 0 for 27C and 1 for 35 C]

Estimated difference of counts between two experimental times = 71.7 and

Estimated difference of counts between two experimental temperature = 89.1

Based on this model, The combination of time = 48 hours and temp = 35 will yield highest count.

Regression statistics

2. I have installed a fifth data of interacton term of temp and time and rerun the model.

By running multiple linear regression model including interaction term(i have done it in excel)

I got y = - 89.7 + 110.5x + 113.8t + 131.2h - 84.2 th + error

where y = count , x = conc , t = time [ 0 for 24 hours and 1 for 48 hours] and h = [ 0 for 27C and 1 for 35 C]

th = Temperature and Hours [ where 1 for T = 35 C and Hr = 48 hrs and 0 for otherwise]

Estimated difference of counts between two experimental times = 113.8 and

Estimated difference of counts between two experimental temperature = 131.2

Estimated difference of counts when temp =1 and time = 1 and othewise = 113.8 + 131.2 - 84.2 = 160.8

Based on this model, The combination of time = 48 hours and temp = 35 will yield highest count.

p - value for testing the interaction = 0.0276 and this suggests that this interaction term is significant in nature and it tells that it gives perfect environment for increaased bacteria count when there is perfect temprature and perfect hours time given to it.

Based on this model also the best combination is same where time = 48 hours and temp = 35

Coefficients Standard Error t Stat P-value Intercept -68.65 38.88031214 -1.76568 0.096523 conc 110.5 34.91555102 3.164779 0.006006 temp 71.7 19.75121832 3.630156 0.002251 hours 89.1 19.75121832 4.511114 0.000355

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