Question

solve using r if coding is required

The data in air-pollution.txt are 42 measurements on air-pollution variables recorded at noon in the Los Angeles area on different days.

Variables: X₁ = Wind, X₂ = Solar radiation, X₃ = Carbon monoxide, X₄ = Nitric oxide, X₅ = Nitrogen dioxide, X₆ = Ozone, and X₇ = Hydrocarbon content.

(a) Evaluate the sample mean vector x.

(b) Evaluate the sample variance-covariance matrix, S, and its inverse, S−1.

(c) Evaluate the sample correlation matrix R. Interpret the pairwise correlations. Also con- struct a scatterplot matrix (a matrix of scatter plots) for these data

(d) Construct a normal quantile plot (Q-Q plot) for the solar radiation measurements (X2) and carry out a test for normality using the Shapiro-Wilk test. Does the data appear to be normally distributed? Explain.

data is

Wind Radiation CO NO NO2 O3 HC
  8  98  7  2  12  8  2
  7  107  4  3  9  5  3
  7  103  4  3  5  6  3
  10  88  5  2  8  15  4
  6  91  4  2  8  10  3
  8  90  5  2  12  12  4
  9  84  7  4  12  15  5
  5  72  6  4  21  14  4
  7  82  5  1  11  11  3
  8  64  5  2  13  9  4
  6  71  5  4  10  3  3
  6  91  4  2  12  7  3
  7  72  7  4  18  10  3
  10  70  4  2  11  7  3
  10  72  4  1  8  10  3
  9  77  4  1  9  10  3
  8  76  4  1  7  7  3
  8  71  5  3  16  4  4
  9  67  4  2  13  2  3
  9  69  3  3  9  5  3
  10  62  5  3  14  4  4
  9  88  4  2  7  6  3
  8  80  4  2  13  11  4
  5  30  3  3  5  2  3
  6  83  5  1  10  23  4
  8  84  3  2  7  6  3
  6  78  4  2  11  11  3
  8  79  2  1  7  10  3
  6  62  4  3  9  8  3
  10  37  3  1  7  2  3
  8  71  4  1  10  7  3
  7  52  4  1  12  8  4
  5  48  6  5  8  4  3
  6  75  4  1  10  24  3
  10  35  4  1  6  9  2
  8  85  4  1  9  10  2
  5  86  3  1  6  12  2
  5  86  7  2  13  18  2
  7  79  7  4  9  25  3
  7  79  5  2  8  6  2
  6  68  6  2  11  14  3
  8  40  4  3  6  5  2

Answer 1