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Solutions to Homework 2

 

(Solutions written by grader for Section 002)

 

1.     Do you think x and ya are positively correlated? If correlation is present, is it positive or negative?

 

By the plot of ya*x, there is positive correlation between x and ya

 

2.     Do you think x an yb are positively correlated? If correlation is present, is it negative or positive?

 

The plot of yb*x shows positive correlation between x and yb. Yb has a quadratic relationship with x.

 

3.     Do you think x and yc are positively correlated? If correlation is present, is it negative or positive?

 

There is positive correlation between x and yc.

 

4.     Do you think x1 and y1 are positively correlated? If correlation is present, is it negative or positive?

 

If the outlier is ignored, it appears that there is positive correlation between these two variables.

 

5.     For the data set x and ya, calculate the correlation coefficient by hand. You can get SAS to calculate some of the values for your hand computation. Interpret the value that you calculated.

 

r = sxy / sqrt(sxxsyy) = 0.8164

 

This value tells us that there is a fairly strong, positive correlation between x and ya.

 

6.     Use PROC CORR to calculate the correlation for each pair of variables. Report the correlation and the p-value for each pair.

 

 

Correlation

p-value

X with Ya

0.816

0.0022

X with Yb

0.816

0.0022

X with Yc

0.816

0.0022

x1 with y1

0.816

0.0022

 

7.     Use PROC REG to fit a regression line to each set of data. Report the equation of the regression line for each data set.

 

Ya = 3.00 + 0.5x

Yb = 3.00 + 0.5x

Yc = 3.00 + 0.5x

Y1 = 3.00 + 0.5x1

 

8.     Create a table summarizing the mean of the independent variable, mean of the dependent variable, equation of the regression line, MSE, R-square, r, std. error of the slope.

 

 

X and ya

X and yb

X and yc

X1 and y1

Mean ind var

9.000

9.000

9.000

9.000

Mean dep var

7.501

7.501

7.501

7.501

Reg. eqn.

See above

 

 

 

MSE

1.530

1.531

1.528

1.527

R-square

0.667

0.666

0.666

0.667

r

0.816

0.816

0.816

0.817

se(slope)

0.118

0.118

0.118

0.118

 

9.     What would happen to the value of the MSE if we fit a curve, possibly a quadratic, to the data for x and yb?

 

The MSE will decrease

 

10. Write 2 or 3 sentences about how you would handle the outlier in the data set for x and yc.

 

First, check the data to determine whether the point truly is an outlier (e.g., could it have been a data entry error which could be corrected, or is it really a realistic value for the data). If it is an outlier, remove it from the data set and re-fit the regression line.

 

11. What would happen if that observation was deleted?

If y1 is deleted, then the fitted regression line would be perpendicular to the x1 axis.