Question 1: The following table gives measurements of the area ( x in km 2 ) and p H level ( y) of 13 lakes in Ontario, Canada. ( hand calculation in nothing else is stated)

Ar ea( x)	33	161	189	149	47	170	352	187	76	52	175	53	200
p H( y)	6 . 6	6 . 4	6 . 5	6 . 9	7 . 1	7 . 5	8 . 8	6 . 4	5 . 9	6 . 7	7 . 1	6 . 6	8 . 0

) Sketch the scatterplot of y vs x and comment on the plot. ( use Minitab or R/ Rstudio)
) Use the Principle of Least Squares to f it the simple linear regression model to the data. Superimpose this line of best f it on the scatterplot in part ( a).
) Perform an ANOVA test to deduce whether there is a l inear relationship between area and p H level.
) Perform all appropriate residual checks using R/ Rstudio or MINITAB and clearly explain if any of the model assumptions have been violated.
) Another lake in the same region was found to have an area of 2050 km 2. Predict its p H level and f ind a 99% confidence interval of this prediction.

( 3 + 8+ 5 + 8+ 3 = 27)

Where X represent the steam in pounds per months and Y is the mean atmosphere temperature measured in Fahrenheit.
Calculate the followings:

Fit a l inear regression model and give the least square estimates for the constant and the slope.
Calculate the residuals for each of the 25 observations.
Make the ANOVA table and complete it by performing all the required calculations. W hat is the ANOVA table used for?
Find the coefficient of determination and the correlation coefficient. Explain its value.
Calculate the std for the error, the std for the slope and the std for the constant.
Test whether the slope and the constant are significant. State the needed hypotheses and explain your results.
Construct the confidence intervals for the slope and for the constant.

( 8 + 4+ 6 + 4+ 6 + 4+ 6 = 38 )

Generate a scatterplot of the data and comment on it .
Answer all the queries a)- g) of Question 2 and comment on the derived outputs.
Using the generated residuals, test the assumption behind the simple linear regression.

( 2 + 26+ 7= 35)