MET CS 555 Assignment 3 solution

Description

The data in this document gives the number of meals eaten that contain fish (per week) and mercury levels in head hair for 100 fisherman.  Save the data to a format that can be read into R.  Read the data in for analysis.  Use R to calculate the quantities and generate the visual summaries requested below. 

(1) Save the data to a file  (excel or CSV file) and read it into R memory for analysis. (Q1 –  2 points)

(2) To get a sense of the data, generate a scatterplot (using an appropriate window, label the axes, and title the graph).  Consciously decide which variable should be on the -axis and which should be on the y-axis.  Using the scatterplot, describe the form, direction, and strength of the association between the variables. (Q2 – 3 points)

(3) Calculate the correlation coefficient.  What does the correlation tell us? (Q3 – 2 points)

(4) Find the equation of the least squares regression equation, and write out the equation.  Add the regression line to the scatterplot you generated above. (Q4 – 4 points)

(5) What is the estimate for  beta_1 ?   How can we interpret this value?  What is the estimate for beta_0 ?  What is the interpretation of this value?  (Q5 – 4 points)

(6) Calculate the ANOVA table and the table which gives the standard error of   (hat beta 1) .  Formally test the hypothesis that beta_1 = 0 using either the F-test or the t-test at the  alpha level a=0.10.  Either way, present your results using the 5 step procedure as in the course notes.  Within your conclusion, calculate the R²    (R  squared) value and interpret this.

Also, calculate and interpret the 90% confidence interval for  beta_1 .   (Q6 –  5 points)