Calculators are allowed, you will have the normal and chi-squared tables (for the previous problems).
The following five problems refer to the data set {(1,3), (3,1), (4,0), (-1,4)}. Recall that the least squares regression line y-hat = b_0 + (b_1)(x) is calculated from the formulae: b_1 = SSxy/SSxx; b_0 = y-bar - (b_1)(x-bar); r = SSxy/(SSxxSSyy)^.5; and r^2 = SS{y-hat}{y-hat}/SSyy.
1) What is the slope of the regression line (b_1)?
0
.4
-.4
.8
-.8
2) What is the y-intercept (b_0) of the least squares regression line?
0
1.8
2.4
3.4
5.2
3) What is the coefficient of determination (r^2) of x and y?
.98
-.98
.99
-.99
1.00
4) What is the standard deviation of the x values (s_x)?
1.5
1.8
2.2
3.3
4.9
5) Use the least squares regression line to estimate the value of y associated with x=2
0.8
1.5
1.8
3.4
3.6
The following three problems refer to the data sets displayed below:
6) Which data set has the greatest slope of the least squares regression line?
7) Which data set has the greatest coefficient of determination (r^2)?
8) which data set has the smallest standard deviatioj of the x-coordinates?
9) If the slope of the least squares regression line is negative, what else must be negative?
The correlation (r)?
The coefficient of determination (r^2)?
The y-intercept (b_0)
More than one of the above must be negative.
None of the above need be negative.
10) What must be true if all the data lies in the first quadrant?
The mean of the x values (x-bar) is positive.
The slope of the regression line (b_1) is positive.
The correlation (r) is positive.
More than one of the above must be true.
None of the above need be true.