Exercise 6-4. Turbidity is a measure of the cloudiness of the water and is used to indicate water quality levels. Higher turbidity levels are usually associated with higher levels of disease-causing microbes like viruses, bacteria, and parasites. The turbidity units of measure are reported as formazin suspension units, or FAUS. Data were collected on the Rio Grande River during the late spring and summer moths in order to study the relationship between temperature and turbidity. The data follow. Temperature Turbidity Temperature Turbidity y y 22.9 125 26.1 100 24.01 118 26.9 105 22.9 103 22.8 55 23.0 105 27.0 267 20.5 26 26.1 286 26.2 90 26.2 235 25.8 99 26.6 265 Summary statistics are given below: n=14,x=347,x=8655.02, y = 1979, y=372345, x,y,=50482 The model assumed is y =ẞ, +ẞ₁x+& where represents random errors that are independently distributed Normal with mean 0 and variance o². a. b. C. d. e. f. B- h. Draw a scatter diagram of y (Turbidity) versus x (Temperature). Does a linear relationship between x and y seem reasonable in this situation? Perform the hand calculations to compute the least-squares line. Draw this line on your plot in (a). (You should get ŷ=-510.7+26.31x.) Calculate by hand the sample correlation r. By hand, compute SSE and an estimate of a². (You should get SSE-54963.3, & 4580.3.) Find the predicted turbidity associated with a temperature of 25. Compute the residual for the observation y=105 at temperature x=26.9. Compute the coefficient of determination R². Use this number to comment briefly on the strength of the linear relationship. A plot of the residuals versus predicted values is given below left. Does this plot suggest possible problems with the model (i.e. are there any model assumptions that may be violated)? i. j. A normal probability plot of the residuals is given above right. Comment on this plot. Compute seẞ.). (You should get 9.178) k. Compute a 95% 2-sided Cl for ẞ1. 1. Test the hypothesis Ho:ẞ:=0 versus H.:ẞ*0 with a=.05. m. In a few sentences, use the above numerical and graphical results to give an overall assessment of the fit of the linear model to the data.