3.The following table gives data on the concentration of chlorophyll-a in a lake along with the concentration of phosphorus in the lake (Source: Smith and Shapiro 1981). Chlorophyll-a is used as an indicator of water quality that measures the density algal cells. Phosphorus stimulates algal growth. We want to use a simple linear regression model to model the relationship between chlorophyll-a and phosphorus in the lake. Please analyze the data and answer the questions.

Data:

Obschlorphoslog(chlor)log(phos)

195.0329.04.553885.79606

239.0211.03.663565.35186

327.0108.03.295844.68213

412.920.72.557233.03013

534.860.23.549624.09767

614.926.32.701363.26957

7157.0596.05.056256.39024

85.139.01.629243.66356

910.642.02.360853.73767

1096.099.04.564354.59512

117.213.11.974082.57261

12130.0267.04.867535.58725

134.714.91.547562.70136

14138.0217.04.927255.37990

1524.849.33.210843.89792

1650.0138.03.912024.92725

1712.721.12.541603.04927

187.425.02.001483.21888

198.642.02.151763.73767

2094.0207.04.543295.33272

213.910.51.360982.35138

225.025.01.609443.21888

23129.0373.04.859815.92158

2486.0220.04.454355.39363

2564.067.04.158884.20469

"Q6.txt"provides you the above data. Use the following code to load the data to R.

> setwd("C:\\biostat_intro_2019\\final")

## change to your specific path where you saved the data

> data<-read.table("Q6.txt", header=T)

a)Provide and examine the scatterplots of chlorophyll-a vs. phosphorus (column 2 and 3) and log(chlorophayll-a) vs. log(phosphorus) (column 4 and 5).Determine whether a linear model adequately describes the relationship between chlorophyll-a and phosphorus or their log transformed data.

b)Provide the fitted linear regression equation estimate relating whatever you determined in question a.

c)Perform the t test to check whether the slope of the regression is significant.Write down the null and alternative hypothesis that is being tested with thist-test statistic. Report the p-value and your conclusion.

d)What is the predicted amount of the average chlorophyll-a given the concentration of phosphorus is 200?