Using the data and model fit in problem 9.8 (book- Applied linear regression by Standford Weisberg), do the following:

a. Perform a test for outliers and interpret the test's results.

b. Determine whether any observations are highly influential, as measured by Cook'sD.

c. Perform a Durbin-Watson test of independence in the residuals and interpret the test's results

d. Obtain a normal probability plot and perform a Shapiro Wilk test of normality in the residuals. Interpret the test's results and the plot.

(code as example: Model <- lm(age ~ circumference + Tree, data = Orange), shapiro.test() or shapiro.test(residuals(Model))

e. Perform a test for non-constant variance in the residuals-vs.-fitted values plot. Interpret the test's results.

f. Summarize all your findings from the diagnostics of this model and make a recommendation about whether this model's results should be trusted.

fitted value- residulaPlots(lm(log(BSAAM)~log(APMAM)+log(APSAB)+log(APSLAKE)+log(OPBPC)+log(OPSLAKE), data=water), fitted=FALSE, quadratic=FALSE)

Data: water (1-45 just the number of rows) data 'water' can be found in library(alr4) in Rstudio

water>> Year APMAM APSAB APSLAKE OPBPC OPRC OPSLAKE BSAAM 1 1948 9.13 3.58 3.91 4.10 7.43 6.47 54235 2 1949 5.28 4.82 5.20 7.55 11.11 10.26 67567 3 1950 4.20 3.77 3.67 9.52 12.20 11.35 66161 4 1951 4.60 4.46 3.93 11.14 15.15 11.13 68094 5 1952 7.15 4.99 4.88 16.34 20.05 22.81 107080 6 1953 9.70 5.65 4.91 8.88 8.15 7.41 67594 7 1954 5.02 1.45 1.77 1 3.57 12.45 13.32 65356 8 1955 6.70 7.44 6.51 9.28 9.65 9.80 67909 9 1956 10.50 5.85 3.38 21.20 18.55 17.42 92715 10 1957 9.10 6.13 4.08 9.55 9.20 8.25 70024 11 1958 8.75 5.23 5.90 15.25 14.80 17.48 99216 12 1959 8.10 3.77 4.56 9.05 6.85 9.56 55786 13 1960 3.75 1.47 1.78 4.57 6.10 7.65 46153 14 1961 10.15 5.09 4.86 8.90 7.15 9.00 47947 15 1962 6.15 3.52 3.30 16.90 14.75 17.68 76877 16 1963 12.75 8.17 10.16 16.75 11.55 15.53 88443 17 1964 7.35 4.33 4.85 5.25 7.45 8.20 54634 18 1965 11.25 6.56 7.60 8.40 13.20 13.29 78806 19 1966 4.05 1.90 2.00 10.85 8.25 12.56 56542 20 1967 12.65 6.62 7.14 23.25 17.00 23.66 116244 21 1968 4.65 3.84 3.34 7.10 6.80 8.28 60857 22 1969 5.35 3.62 4.62 43.37 24.85 33.07 146345 23 1970 4.05 1.98 2.94 8.95 11.25 11.00 73726 24 1971 5.90 5.72 5.42 8.45 10.90 10.82 65530 25 1972 9.45 4.82 6.79 7.90 7.60 8.06 60772 26 1973 3.45 2.63 2.88 14.80 14.70 15.86 91696 27 1974 4.25 2.54 2.36 18.05 16.90 16.42 87377 28 1975 7.90 4.42 6.78 11.50 9.55 12.56 77306 29 1976 9.38 8.30 9.70 6.80 5.25 4.73 44756 30 1977 7.08 4.40 3.90 4.05 4.35 4.60 41785 31 1978 11.92 5.78 6.70 25.30 20.55 21.94 112653 32 1979 3.88 2.26 3.10 15.97 11.83 13.88 79975 33 1980 5.80 3.10 3.34 24.40 19.15 23.78 106821 34 1981 2.70 2.22 2.48 8.99 9.45 12.14 69177 35 1982 18.08 11.96 13.02 18.55 18.40 19.45 120463 36 1983 8.20 4.98 5.76 19.25 22.90 23.86 135043 37 1984 7.65 5.30 5.74 14.45 13.15 14.42 102001 38 1985 5.22 4.42 4.04 11.45 10.16 13.06 77790 39 1986 4.93 3.26 4.58 26.47 15.33 26.46 118144 40 1987 5.99 2.76 3.98 4.80 6.85 6.36 61229 41 1988 6.83 6.82 5.18 7.20 9.01 9.88 58942 42 1989 8.80 5.06 4.92 8.05 9.60 9.58 53965 43 1990 7.10 5.06 6.05 5.80 6.50 8.41 49774