Question

Problem 3. (Selenium in the Sea) Selenium (Se) is an essential element that has been shown to play an important role in protecting marine mammals against the toxic effects of mercury (Hg) and other metals. It has been suggested that metal concentrations in marine mammal teeth (Teeth Se) are positively associated with body burden (Liver Se). Twenty belugas (Delphinapterus leucas) were harvested from the Mackenzie Delta, Northwest Territories, in 1996 and 2002, as part of an annual traditional Inuit hunt. A scatterplot and a summary of tooth and liver Se concentrations are reported in the table and the R output. 180 200 220 240 Tooth Se 120 140 160 10 20 30 40 Liver Se 1 X; (Liver Se, ug/g) 6.23 Y; (Tooth Se, ng/g) 140.16 2 ... 20 6.79 ... 45.47 133.32 ... 141.31 Mean V ariance T = 20.685 S = 13.4491 | = 156.599 S = 36.0595 Coefficients: Estimate Std. Error t value Pr(>t) (Intercept) 126.801 13.052 9.7151.39e-08 *** LiverSe 1.441 0.533 2.703 0.0146 * Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1 Residual standard error: 31.25 on 18 degrees of freedom (a) Write the equation for the least squares regression line. (Hint: The estimates for the intercept and slope are in the R output.) (b) Interpret the physical meaning of the intercept and slope in this regression. (d) Recall that a general form of a confidence interval is estimate critical value x SE(estimate). With this in mind, create a 95% confidence interval for the true slope, B1, using the least squares estimate. You may assume that the critical value is t18.0.025, and the standard error of B, is 0.533.

Answer 1

critical value is calculated by using t distribution table

ca) y = intercept t slope * x = 126.801 + 1.441 I (b) intercept is the the value of x mean value of Y when estimated is zero slope value it of Y estimates as a the change in the average result of a one unit increase co) estimate t critical value & SEC estimate) 1.441 I 2.101 X 0.533 , 1.4.4 1. 120 I The 95% confidence interval is (0.321, 2.561)