Question

Q) The CO2 dataset in R has data on plants from Quebec and Mississippi (denoted by the variable name 'Type') that were subjected to two different treatments (denoted by the variable name “Treatment"), chilled or nonchilled. I ran two regression models to see what variables best describe CO2 uptake of plants, given different conditions, with the output below: Call: lm(formu la uptakeconcTreatmentType, data-CO2) Residuals: -17.344 2.826 1.070 4.137 11.267 Coefficients: Min 1Q Median 3Q Max Estimate Std. Error t value Prolt (Intercept) conc Treatmentchilled-6.859524 1.351439-5.076 2.46e-06 TypeMississippi 12.659524 1.351439 -9.367 1.67e-14*** 29.259814 1.538928 19.013 <2e-16 0.017731 0.0022977.719 2.87e-11 Signif. codes: 0.0010.01 0.05.0.1''1 Residual standard error: 6.193 on 80 degrees of freedom Multiple R-squared: 0.6839, Adjusted R-squared: 0.6721 F-statistic: 57.7 on 3 and 80 DF, p-value: 2.2e-16 AICC1m(uptake conc+Treatment Type, dataCO2) 550.6198 Model 1 Results: Call: 1m(formu la uptakeconcTreatment, data Co2) Residuals: 19.401 7.066 -1.168 7.573 17.597 Coefficients: 3Q Min 1Q Median Max Estimate Std. Error t value Pr(ItI (Intercept) conc Treatmentchilled-6.8595241.944840-3.527 0.000695 22.930052 1.989746 11.524 <2e-16 0.017731 0.003306 5.364 7.55e-07 Signif. codes: 0.0010.010.050.1''1 Residual standard error: 8.912 on 81 degrees of freedom Multiple R-squared: 0.3372,Adjusted R-squared: 0.3208 F-statistic: 20.6 on 2 and 81 DF, p-value: 5.837e-08 AICC1m(uptake conc +Treatment, data co2) 1 610.8169 Model 2 Results: a. What are the regression equations for models 1 and 2? b. What kind of variable is "Treatment"? c. What does the sign of the Treatment variable mean for CO2 uptake? d. Based off of the AIC which model better explains CO2 uptake? e. Based off of the Adjusted R-squared which model better explains CO2 uptake?

Q) The CO2 dataset in R has data on plants from Quebec and Mississippi (denoted by the variable name ‘Type’) that were subjected to two different treatments (denoted by the variable name “Treatment”), chilled or nonchilled. I ran two regression models to see what variables best describe CO2 uptake of plants, given different conditions, with the output below:

1. What are the regression equations for models 1 and 2?
2. What kind of variable is “Treatment”?
3. What does the sign of the Treatment variable mean for CO2 uptake?
4. Based off of the AIC which model better explains CO2 uptake?
5. Based off of the Adjusted R-squared which model better explains CO2 uptake?

Answer 1

What are the regression equations for models 1 and

Model 1:
uptake = 29.2598 + 0.0177 conc - 6.8595 Treatment - 12.6595 Type

Model 2 :
uptake = 22.93+ 0.0177 conc - 6.8595 Treatment

What kind of variable is “Treatment”?
Binary variable

What does the sign of the Treatment variable mean for CO2 uptake?
When the treatment change from nonchilled to chilled, the uptake decrease by 6.85.(negative sign indicates the decrease)

Based off of the AIC which model better explains CO2 uptake?

Model1: 550.6198
Model2 : 610.8169

Lower the AIC, better is the model. Hence Model 1 is better.

Based off of the Adjusted R-squared which model better explains CO2 uptake?

Model1 : 0.6721
Model2 : 0.3208

Model1 is better based on adjusted r squared.