Question

Please make sure you write the R cude,

R-PROGRAM

Data was collected in order to investigate the effect of temperature on the yield of a chemical process. Temperatures were set at eight specific levels, and the yield was determined for five replications at each evel 4. a. Identify the response variable and the predictor variable. Explain your reasoning b. Describe the two sources of variation (variation due to regression and variation about the regression) in terms of this particular problem (using the variables described above). c. In this particular case, are we investigating for association or causation? Defend your answer The data frame "stackloss" is available in R and contains 21 measurements on each of four variables. For this problem, we are only interested in determining if there is a relationship between stack.loss (energy 5. loss) and Water.Temp (cooling water temperature) a. Obtain a scatter plot of the variables stack.loss (vertical axis) versus Water.Temp (horizontal axis) b. Based on the graph in (a), how would you describe the apparent relationship between stack.loss c. Use the Im function in R to determine the sample regression equation, and plot the sample Give the plot the title "Problem 4.a", and label the axes appropriately and Water.Temp? regression equation on the scatterplot obtained in (a). Comment on how well (or poorly) the sample regression fits the data. d. Verify that the sample regression equation passes through (X,).

Answer 1

Ques 5

R codes

> data("stackloss")
> data = stackloss
> head(data)
Air.Flow Water.Temp Acid.Conc. stack.loss
1 80 27 89 42
2 80 27 88 37
3 75 25 90 37
4 62 24 87 28
5 62 22 87 18
6 62 23 87 18
> attach(data)
The following object is masked _by_ .GlobalEnv:

stack.loss

The following objects are masked from data (pos = 3):

Acid.Conc., Air.Flow, stack.loss, Water.Temp

The following object is masked from package:datasets:

stack.loss

> plot( Water.Temp,stack.loss, main = 'problem 4.a',xlab = 'Water.Temp', ylab = 'stack.loss', lwd = 2)
> cor(Water.Temp,stack.loss)
[1] 0.8755044

b) There is linear relationship between two variables.

c)

Sample reg equation:

> reg = lm(stack.loss~Water.Temp)
> reg

Call:
lm(formula = stack.loss ~ Water.Temp)

Coefficients:
(Intercept) Water.Temp
-41.911 2.817

> plot( Water.Temp,stack.loss, main = 'problem 4.a',xlab = 'Water.Temp', ylab = 'stack.loss', lwd = 2)
> abline(reg, col='red', lwd = 2)
>

From plot we can see that sample regression fits the data quite well.

d)

> plot( Water.Temp,stack.loss, main = 'problem 4.a',xlab = 'Water.Temp', ylab = 'stack.loss', lwd = 2)
> abline(reg, col='red', lwd = 2)
> abline(v = mean(Water.Temp))
> abline(h = mean(stack.loss))

Thus sample regression equation passes through $\small (\hat{X},\hat{Y})$ = (mean(Water.Temp),mean(stack.loss))

> mean(stack.loss)
[1] 17.52381
> mean(Water.Temp)
[1] 21.09524