A) Calculate the standard errors of ˆα and βˆ.B) Use a t-test to test H0 : β = 0 versus H1 : β < 0 with significance level 5%. We are interested in using the pH of the lake water (which is easy to measure) to predict theaverage mercury level in fish from the lake, which is hard to measure. Let x be the pH of thelake water and Y be the average mercury level in fish from the lake. A sample of n = 10 lakesyielded the following data:Observation (i)13456810pH (x;)Average mercury level (y;) 0.158.28.47.07.27.36.49.15.87.68.10.040.400.500.270.810.040.830.050.19Suppose we fit the data with the following regression model:Y; = a + Bx;+ Ei, i =1,..., 10,where ɛi ~· N(0, o²)are independent. We have the following quantities: ī = E–1 Xi = 7.51,n Li=1vi=1i=1i=1Some R output that may help.> p1 <- c(0.01, 0.025, 0.05, 0.1, 0.9, 0.95, 0.975, 0.99)> qt (p1, 8)[1] -2.896 -2.306 -1.860 -1.3971.3971.8602.3062.896> qt (p1, 9)[1] -2.821 -2.262 -1.833 -1.3831.3831.8332.2622.821

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Answered: Calculate the standard errors of ˆα and…

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Calculate the standard errors of ˆα and βˆ.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter2: Exponential, Logarithmic, And Trigonometric Functions

Section2.CR: Chapter 2 Review

Problem 111CR: Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data...

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A group of researchers studied the effect of acid rain on wildlife and collected n = 12 samples from streams in different States. They recorded the pH (X) of the water (i.e. units above pH 7), and the BCI, a measure of biological diversity (Y). The data obtained is summarized below. DATA: Observation 1 2 3 4 5 6 7 8 9 10 11 12 pH above 7 (X) 0.67 0.70 0.93 0.95 1.09 1.01 1.29 1.24 1.41 1.56 1.73 1.80 Units of BCI (Y) 14.4 20.9 16.2 25.0 18.9 19.8 20.7 22.1 23.9 24.9 27.6 29.7 Find the correlation coefficient between pH and BCI (round to the nearest hundredth; place your answer in the box below)