Recall the GSS (General social survey) data, where respondents were asked the extent of confidence they had in various U.S. institutions. For the questions here, we consider only the education and scientific institutions but all three responses ("great deal", "hardly any", "only some"). The data can be read in and summarized with the commands below.

gss = read.csv(file.choose(), header=T) # "gss.confidence.csv" gss = gss[gss$question!='conmedic',] table(unstack(gss[,c(5,4)]))

Please answer all the questions with R and provide all the R codes, thank you.

(a) Report and interpret the Kappa coefficient between the two institutions.

(b) What would "symmetry" mean in the context of this situation? Is it a reasonable assumption in this case? State appropriate log-linear models to test this, and carry the test out at the 0.05 level.

(c) Report the estimated counts for the 3 3 table between education and scientific institutions under the symmetry mode

(d) Consider the model below log(j/3)= 0j + 1j x1 + 2j x2, j = 1, 2

where j is the probability of confidence level j (1="hardly any", 2="only some", 3="great deal") in education institutions, x1 is an indicator for "hardly any" confidence in scientific institutions, and x2 is an indicator for "only some" confidence in scientific institutions.

In the context of the variables here, what assumption does the hypothesis H0 : 1j =2j = 0 for j = 1, 2 correspond to? Carry out this test relative to the model above, and comment on what (if any) connection this test has to the one above in part (b)

Thank you!