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 months in order to study the relationship between temperature and turbidity. The data follow.

(a) Estimate the intercept 0 and slope 1 regression coefficients.
Write the estimated regression line.

(b) Compute the residuals.

(c) Compute SSE and estimate the variance.

(d) Find the standard error of the slope and intercept coefficients.

(e) Show that SST SSR SSE.
(f ) Compute the coefficient of determination, R2. Comment on the value.
(g) Use a t-test to test for significance of the intercept and slope coefficients at 0.05. Give the P-values of each and comment on your results.
(h) Construct the ANOVA table and test for significance of regression using the P-value. Comment on your results and their relationship to your results in part (g).
(i) Construct 95% CIs on the intercept and slope. Comment on the relationship of these CIs and your findings in parts (g) and (h).
(j) Perform model adequacy checks. Do you believe the model provides an adequate fit?
(k) Compute the sample correlation coefficient and test for its significance at 0.05. Give the P-value and comment on your results and their relationship to your results in parts (g) and (h).

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Temperature Turbidity Temperature Turbidity x y x 22.9 125 26.1 100 24.0 118 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