Question

1. Consider data from a study of the association between vapor pressure (in mm and temperature (in degrees K). The vapor pressure y is the response and the temperature x is the predictor. We import the data with R and display a few rows. Hg) of water > vapor head(vapor) Temp.. in.K. Vapor.Pressure 4.6 1 273 283 9.2 2 3 293 17.5 4 303 31.8 313 55.3 323 92.5 (a) Here is a scatter plot of vapor pressure against temperature. Does it seem likely that a simple linear regression model of vapor pressure as a linear function of temperature will be adequate? 090 0 320 280 300 340 360 Temperature (in K) w (b) Here are a few residual plots and some statistical diagnostic test. Discuss the resulting residual analysis. What are your conclusions concerning model adequacy? Residuals ys Fitted Scale-Location .100 0 100 200 308 400 600 .100 100 200 300 400 s Fmed values Fted vaues tCuantles > mod par (mfrow=c(1,3)) > plot (mod,which=c(1,3)) > library(car) > qqPlot (mod) [1] 1 11 > library (1mtest) > resettest (mod) RESET test data: mod RESET 1974.3, dfi 2, df2 7, p-value = 2.331e-10 = = bptest (mod) studentized Breusch-Pagan test data mod BP 1.6445, df 1, p-value 0.1997 = > shapiro.test (rstandard (mod)) Shapiro-Wilk normality test data W = 0.9037, p-value rstandard (mod) 0.205

Answer 1

a) from the scatter plot we see that the value of vapor pressure is gradually going higher with increase in temperature. so there exists a positive correlation between them. But in order to justify it by a linear model it will wrong because the plot shows curve not the linearity. So linear regression between vapor pressure and temperature is not adequate.

B)from the 1st plot errors and fitted values are correlated but non linearity exists . so linear regression fails.

from the scale location plot we see that there exists no uniformity in variances throughout our predictor range so heteroscedasticity exists