For my adv stat assignment, I worked with a dataset with the goal to use multiple linear regression and ANOVA to see how age, weight, bmp, and fev1 relate to pemax.
##Load the ISwR package
library(ISwR)
## Load the cystfibr dataset data
(“cystfibr”, package = “ISwR”)
Output:
age sex height weight bmp fev1 rv frc tlc pemax
1 7 0 109 13.1 68 32 258 183 137 95
2 7 1 112 12.9 65 19 449 245 134 85
3 8 0 124 14.1 64 22 441 268 147 100
4 8 1 125 16.2 67 41 234 146 124 85
5 8 0 127 21.5 93 52 202 131 104 95
6 9 0 130 17.5 68 44 308 155 118 80
7 11 1 139 30.7 89 28 305 179 119 65
8 12 1 150 28.4 69 18 369 198 103 110
9 12 0 146 25.1 67 24 312 194 128 70
10 13 1 155 31.5 68 23 413 225 136 95
11 13 0 156 39.9 89 39 206 142 95 110
12 14 1 153 42.1 90 26 253 191 121 90
13 14 0 160 45.6 93 45 174 139 108 100
14 15 1 158 51.2 93 45 158 124 90 80
15 16 1 160 35.9 66 31 302 133 101 134
16 17 1 153 34.8 70 29 204 118 120 134
17 17 0 174 44.7 70 49 187 104 103 165
18 17 1 176 60.1 92 29 188 129 130 120
19 17 0 171 42.6 69 38 172 130 103 130
20 19 1 156 37.2 72 21 216 119 81 85
21 19 0 174 54.6 86 37 184 118 101 85
22 20 0 178 64.0 86 34 225 148 135 160
23 23 0 180 73.8 97 57 171 108 98 165
24 23 0 175 51.1 71 33 224 131 113 95
25 23 0 179 71.5 95 52 225 127 101 195
##Create the multiple linear regression model
model <- lm(pemax ~ age + weight + bmp + fev1, data = cystfibr)
summary(model)
Output:
Residuals:
Min 1Q Median 3Q Max
-42.521 -10.885 3.003 15.488 41.767
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 179.2957 61.8855 2.897 0.00891 **
age -3.4181 3.3086 -1.033 0.31389
weight 2.6882 1.1727 2.292 0.03287 *
bmp -2.0657 0.8198 -2.520 0.02036 *
fev1 1.0882 0.5139 2.117 0.04695 *
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 23.4 on 20 degrees of freedom
Multiple R-squared: 0.5918, Adjusted R-squared: 0.5101
F-statistic: 7.248 on 4 and 20 DF, p-value: 0.0008891
This means that weight and fev1 had a positive relationship with pemax, while age and bmp had a negative relationship when the other variables were held constant.
Weight, bmp, and fev1 were statistically significant because their p-values were below 0.05. Age was not statistically significant because its p-value was 0.3139. The R-squared value was 0.5918, meaning that about 59.2% of the variation in pemax can be explained by age, weight, bmp, and fev1. The overall regression model was also statistically significant because the p-value was 0.0008891.
Run the ANOVA for the regression model
anova(model)
Output:
Analysis of Variance Table
Response: pemax
Df Sum Sq Mean Sq F value Pr(>F)
age 1 10098.5 10098.5 18.4385 0.0003538 ***
weight 1 945.2 945.2 1.7258 0.2038195
bmp 1 2379.7 2379.7 4.3450 0.0501483 .
fev1 1 2455.6 2455.6 4.4836 0.0469468 *
Residuals 20 10953.7 547.7
—
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
The ANOVA results were slightly different from the regression results. Age was statistically significant with a p-value of 0.0003538, while weight was not significant with a p-value of 0.2038. BMP was very close to the 0.05 cutoff with a p-value of 0.0501, and fev1 was statistically significant with a p-value of 0.0469.
Overall, the results show that the variables in the model explain a good amount of the variation in pemax. The regression results showed that weight, bmp, and fev1 were significant predictors when the other variables were held constant. The ANOVA results showed that age and fev1 were significant.
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