Module 7

1.1 
Y = a + bX + e 
x <- c(16, 17, 13, 18, 12, 14, 19, 11, 11, 10) 
y <- c(63, 81, 56, 91, 47, 57, 76, 72, 62, 48) 
model1 <- lm(y ~ x) 
summary(model1) 
1.2 
coef(model1) 
Intercept (a) = 14.82lope (b) = 3.74 
Regression Equation: Y = 14.82 + 3.74X 
For every unit increment in the independent variable x, y increases about 3.74 unit compare this with unit regression in the earlier case. 
2. 
The model for predicting eruption duration (discharge) based on waiting time (waiting) is: 
discharge = a + b(waiting) + e 

data(faithful) 

model2 <- lm(eruptions ~ waiting, data = faithful) 
summary(model2) 
2.2 

coef(model2) 

Results: 

  

Intercept (a) = –1.874 

  

Slope (b) = 0.0756 

  

Estimated Regression Equation: 

discharge = –1.874 + 0.0756(waiting) 

 

2.3 

predict(model2, data.frame(waiting = 80)) 

Predicted discharge duration: 4.17 

If the waiting time since the last eruption is 80 minutes, the eruption of the length is expected to be about 4.17 min. This confirms the existence of a positive relationship (after long waits long eruptions). 

 

3 

input <- mtcars[, c("mpg", "disp", "hp", "wt")] 

model3 <- lm(mpg ~ disp + hp + wt, data = input) 

summary(model3) 

Results: 

  

Intercept = 37.11 

  

disp = –0.00094 

  

hp = –0.0312 

  

wt = –3.80 

  

Regression Equation: 

mpg = 37.11 – 0.00094(disp) – 0.0312(hp) – 3.80(wt) 

The coefficients show that the weight (wt.) has the most serious negative effect upon miles/gallon. Thus the greater the weight of the car more serious the fall in miles per gallon. Horse-power (hp) and displacement also have negative effects on M. P. G. but not in so serious an extent. Hence the more satisfactory equation gives a better idea of the manner in which the various independent variables may together produce an effect on fuel consumption. 

 

4. 

library(ISwR) 

plot(metabolic.rate ~ body.weight, data = rmr) 

model4 <- lm(metabolic.rate ~ body.weight, data = rmr) 

abline(model4, col = "red") 

predict(model4, data.frame(body.weight = 70)) 

Results: 

Predicted metabolic rate for 70 kg ≈ 1710 kcal/day 

The regression equation shows a marked positive relation between body weight and basal metabolism.With the increase in body weight shows increase in basal metabolism. A person with a body weight of about 70 Kilos is expected to have a basal metabolism of about 1710 Kcal/day which is unobjectionable for the larger bodies require greater energy in order to maintain their various functions. 

 

Overall takeaway 

in all the examples, the regression equations give a definite idea of how one or more of the predictors have influenced the variations of the dependent variable. The use of R made it possible to examine the coefficients, make predictions, and give an idea of the real relation of the relationships shown in the data. 


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