Lab 3

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Carina Rocha A17544340 Math 11 Section B04 April 10, 2023 The regression equation is BMR = 75.97 + 0.2822 Mass Model Summary S R-sq R-sq(adj) 300.522 84.87% 84.85% Analysis of Variance Source DF SS MS F P Regression 1 303570137 303570137 3361.29 0.000 Error 599 54097824 90314 Total 600 357667961 1. The equation for the regression line is 75.97 + 0.2822 (mass of animal) = basal metabolic rate. My scatterplot shown above displays the basal metabolic rate compared to body mass. 2. The regression line for the Cape Porcupine is 75.97 + 0.2822 (11300) = 3264.83. In this case, the regression equation predicts the correlation between the explanatory variable mass in grams and the responsive variable of BMR in millimeters per hour. Since the

mass is 11300 grams the predicted BMR is about 3000. The San Diego Pocket Mouse has a regression line equation of 75.97 + 0.2822 (19.6) = 81.501. The predicted BMR for the Pokect Mouse is less than 1000. My predictions matched up with the observations from the linear regression. 3. The residual plot is not appropriate for predicting the basal metabolic rate from Mass because its distribution of residuals is cone-shaped. As shown in the residual plot above the variance for residuals increases as the mass increases therefore the plot effectively depicts the data for small masses but not for large masses since the residuals increase from the horizontal line.

The regression equation is LNBMR = 1.474 + 0.6736 LNmass Model Summary S R-sq R-sq(adj) 0.369134 93.04 % 93.03% 4. The histograms with the original variables have a heavy right skewness, resulting in outliers. While the transformed variables have a bimodal distribution. Therefore the transformed variables have a reduced skew compared to the original variables. 5. The regression equation is ln(BMR) = 1.474 + 0.6736 ln(mass) 6. The b value in my regression equation is 0.6736 which is closer to ⅔ supporting my results. 7. In the transformed plots, the residual plot is random and perfectly depicts the data. The randomness means the linear regression has found the best-suited regression line for the data. In the original scatter plot the data only works best for smaller mass but not larger mass as it is harder to estimate since there is no correlation between larger variations. Unlike the transformed scatter plot, the values have a clear correlation near the regression line. As the explanatory variable increases (LN mass)increases so does the responsive variable (LN of BMR), this data is best suited for linear regression since there is a strong correlation between mass and BMR. 8. My predicted equation is BMR = c*(Mass)^b, for the San Diego Pocket Mouse which is BMR =4.36(19.6)^(0.6736). My product was 32.355. For the Cape Porcupine, BMR = 4.36(11300)^(0.6736). My product for the porcupine was 2342.28. Yes, these predictions

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are more accurate than the previous model because this model showcases the distribution evenly. 9. The scatterplot shown above on the right reveals the Blue Whale as an outlier thus I am confident in my prediction of having a low basal metabolic rate. The relationship in the Histogram of Basal Metabolic Rate decreases in BMR when mass increases and increases when the mass decreases. For Rodents The regression equation is BMR = 79.70 + 0.2669 Mass Model Summary S R-sq R-sq(adj) 108.98 2 90.23 % 90.19%

For Primates The regression equation is BMR = 119.4 + 0.3032 Mass Model Summary S R-sq R-sq(adj) 244.43 1 96.57 % 96.42% For Chiroptera The regression equation is BMR = 16.83 + 0.6611 Mass

10. The equation is BMR = 16.83 + 0.6611 (Mass). The scatter plot has a highly positive correlation with some random gaps. There is a linear connection between mass and basal metabolic rate as the mass increases the more dispersed the data is. The regression line is the average of all the data points, as shown above, the increase in mass causes the data to stray away from the average. The residual plot is excellent at illustrating mass less than 2000 grams but as the mass increases the more error. The residual has a distinct distribution called the cone/fanned shape which is not random therefore this linear regression is not appropriate for this data. 11. My estimated allometric exponent for rodents was 79.70 + 0.2669 (Mass) and for the mammals 119.4 + 0.3032 (Mass), these values differ because of the variations in body weight and BMR. My estimated allometric exponent was 0.6000 and my expected was 0.5701. 12. The regression equation is BMR = 119.4 + 0.3032 (Mass). The scatter plot strongly correlates with smaller masses, as BMR increases the further the data is from the regression line. The predicted BMR for a primate that weighs 8100 grams has a BMR of 3900, but as observed the same weight has a BMR of 3200. For the residual plot the data is clustered at small masses and similar to the rodents, has a large difference as the BMR and mass increase. Although the residual plot has a large error all the data in the scatter plot fall within the regression line. Linear regression is an appropriate way to showcase the data. 13. The equation is BMR = 16.83 + 0.6611 (Mass). The scatter plot for Chiroptera is strong at low BMR and mass. There is one influential point that pushed the regression line down. A cluster by the small values and more variation as we increase in both variables. In the residuals plot, there is a large cluster with little difference, units less than 200 and then the data becomes further from the predicted which means the larger data points the more ineffective a residual plot is at displaying the data. The linear regression is not appropriate for this data set. 14. Write a paragraph consisting of several sentences summarizing your conclusions about the relationship between body mass and basal metabolic rate for mammals in general and for the three groups of mammals that you studied in more detail. 15. For mammals in general, basal metabolic rate is a responsive variable because according to the scatter plots the data points are linear with a strong to moderate correlation. In general, the residual plots display a cone-shaped distribution with multiple outliers. This signifies a higher percent error along the scatter plot of mammals. Since the basal metabolic rate is dependent on the grams, but not when the grams are large figures. This tells us that randomness is caused by the explanatory variable. In the Chiroptera, the scatterplot has a lower regression line because of the outlier by the 1000 grams and 800 BMR. Its residual plot has a heavier concentration near 0 which means the predicted data effectively matched the expected but because the plot is heteroscedastic there is a clear

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pattern in the data which means the residual plot is not great with this data. Similarly, the rodents have a cluster for both plots but the rodent’s scatter plot is less compacted among the regression line meaning the is some randomness. For the primates, the scatter plot has a strong correlation but the residual plot has a heteroscedastic distribution which causes more errors and a visual pattern.

Lab 3

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