Name: ________________________
MATH 1203 – Quiz 6
1. Consider the following data, representing an independent (x) and dependent (y) variable. Note that the data has been
augmented to include columns for
2
x
,
2
y
,
yx
, and the respective column totals.
x y x*x y*y x*y
1 9 1 81 9
2 8 4 64 16
3 4 9 16 12
4 3 16 9 12
10 24 30 170 49
The correlation coefficient has been computed to be
265
11
yyxx
xy
SS
S
r
= -0.96476
a) Compute the equation of the least-square regression line y= mx + b
b) Draw a scatter plot for the above data and
draw a regression line “by hand”.
c) Does the value of the correlation coefficient
make sense?
d) Predict the y-value if x = 5. Do you believe
your prediction is accurate? Explain.
2. We want to see if there is a relation between the weight of a car and the average (highway) miles per gallons the car
uses. Several cars, selected at random, were tested, with the results shown as follows:
Model Summary
.874
a
.763 .750 1.8717
Model
1
R R Square
Adjusted
R Square
Std. Error of
the Estimate
Predictors: (Constant), Weight
a.
a) What is the correlation coefficient: r = ______________
b) What is the slope m of the least-square regression line: m = _____________
c) What is the y-intercept b of the least-square regression line: b = ______________
