Psychology 406 Assignment #8

Consider the following set of numbers representing matched observations on two variables:

Variable 1 Variable 2
95  31
100  31
100  31
102  32
103  32
105  32
106  33
106  33
106  33
109  34
110  34
110  34
111  35
112  35
112  35
114  36
114  36
115  36
117  37
118  37
130  37
Variable 1  Variable 2
Sum: 2,295  Sum: 714
Sum Squares: 251,991  Sum Squares: 24,360

Sum of Cross Products: 78,323

i) Construct a scatterplot for these two variables (placing variable 2 along the abscissa — i.e., along the “x axis”).

ii) Find the least-squares line for predicting variable 1 from variable 2 and plot it on the scatterplot constructed in (i).

iii) Calculate the correlation between the two variables and give the percentage of sample variance for variable 1 that is “accounted for” by variable 2 in terms of a linear relationship.

iv) Obtain the usual sample variance of estimate and its unbiased counterpart.