For the x-independent and y-dependent variables listed below

1.For the x-independent and y-dependent variables listed below,
No.  x  y
1  39  65
2  43  78
3  21  52
4  64  82
5  57  92
6  47  89
7  28  73
8  75  98
9  34  56
10  52  75
a)Calculate the mean of x and y.
b)Calculate  Σ x i 2 ,  Σ y i 2 , and  Σ x i y i .
c) Estimate the slope (m) and intercept (c) by the least squares method.
d) Plot the data points and the regression lines
e) What is the residual value when x = 47?
f) What is the sum of squares for error?
g) What is the degree of the freedom?
h) Calculate the variance of the data.
i) Determine whether a linear relationship exists between x and y by using the null
hypothesis.
j) Find a 95 percent confidence interval for c based on the data.
k) Find a 95 percent confidence interval for the expected value of y at x = 50.
l) Calculate the correlation coefficient.
2.The data in the table-below give the moisture contents of samples in a core taken from a
small inlet on the Gulf Coast in eastern Virginia. The measurements were taken immediately
after the samples were removed from the core barrel and forced dried.
Depth (ft) Moisture
(gram/kg dried solid)
0.1000 12.7167
0.2000 12.8760
0.3000 12.5019
0.4000 12.9697
0.5000 12.4105
0.6000 13.3901
0.7000 12.8671
0.8000 13.0331
0.9000 13.8288
1.0000 13.8373
1.1000 13.3454
1.2000 13.2790
1.3000 14.1562
1.4000 13.3807
1.5000 13.3112
1.6000 13.4038
1.7000 12.6431
1.8000 12.3180
1.9000 11.2649
2.0000 11.3883
a)Perform least squares linear regression on this data.
b)Plot the data and linear regression model.
c)Does the model fit the data?
d)Use ANOVA to quantify (c) above.
e)Calculate the correlation coefficient.
f) What model would you recommend for fitting the data?