Make use of R software

A pilot study investigated whether measurements of leaf length and width made in the field could be used to accurately estimate leaf area. Twenty-five plants were chosen at random from a plot of a single variety and the length (cm) and width (cm) of the flag leaf on each plant was measured in situ These leaves were then detached from the plants and their area was measured (cm²) using imaging software. The data contains (variates Leaf, Length, Width, Area).

Leaf Length Width Area

1 28.9 2.4 69.36

2 24.5 2.8 68.6

3 31.7 2.6 82.42

4 29 2.3 66.7

5 28.5 2.5 71.25

6 26.1 2.4 62.64

7 28.6 2.4 68.64

8 26.5 2.6 68.9

9 30 2.7 81

10 27 2.5 67.5

11 28 2.5 70

12 28 2.5 70

13 32 2.7 86.4

14 26.3 2.6 68.38

15 31.2 2.1 65.52

16 29.5 2.6 76.7

17 32.2 2.8 90.16

18 26.5 2,7 71.55

19 33.8 2.7 91.26

20 27.4 2.7 73.98

21 27 2.3 62.1

22 28.9 2.6 75.14

23 32.4 2.4 77.76

24 29.2 2.6 75.92

25 29.8 2.4 71.52

(a) Fit a simple linear regression using the R function lm() to explore the relationship between leaf area and its estimate constructed as length x width. <= (Pay more attention in this question)

(i) Give the fitted model and interpret the regression coefficients.

(ii) Conduct test of hypotheses on the regression coefficients and comment on their significance.

(b) Investigate if the model assumptions satisfied or not using the residual plots. Is there any evidence of outliers?

(c) Plot the observed data with fitted line and showing a 95% pointwise confidence bounds for points on the fitted line. Discuss the result.

(d) In principle, we would expect leaves with zero length or width to have zero area; so, does it make sense to fit regression through the origin in this context? Explain.