PSY 555 Homework 14

Answers

Chapter 9: #10,11,13,14,15,16,18

9.10 _{}

_{}

_{}

_{}

Y=.0689X
+ 3.5306 is the regression equation.

9.11 _{}

_{}

The
standard error of the estimate for the regression equation, Y=.0689X + 3.5306,
is .5803.

9.13. X=70

Y=.0689X
+ 3.5306

Y=.0689(70)
+ 3.5306

Y=8.3536

The
predicted incidence of babies with birth weights less than 2500 grams, if the fertility
rate rises to 70, would be 8.36.

9.14. The
values of X that have been examined in the present study fall between 38 and
56, so the regression equation is based on values within this range. Because we did not examine X values other
than those within this range (i.e., fertility rates around 70) and include such
values when calculating the regression equation, we cannot be sure what the
data does at values around 70 or that the regression equation (if recalculated
to include values such as 70) would even be the same. Therefore, we should not
be confident making a prediction about the incidence of low birthweight
babies if the fertility rate was 70 because we would be extrapolating way
beyond the range of the data on which the equation is based.

9.15.
X_{}=8

_{} _{}

_{} _{}

_{} _{}

_{} _{}

_{} N=107

_{}

_{}

_{}

_{}

_{}

The prediction number of symptoms for an
individual with a stress score of 8 would be 80.2.

9.16. _{}

The predicted value of Y when _{} would be 90.704, which
is essentially equal to the mean of Y (_{}). This makes sense
because the predicted value of Y, given the mean value of X, will be the
average value of Y (since that will be a point on the regression line since the
line is based on information) involving the means of X and Y).

9.18.
.9X+15=1.5X+10

__-9X -10 -.9X-10__

5=.6X

X=8.3_{}

The equations allow us to determine that at
8.33 years faculty and administrators have equal salaries, but after 8.33
years, the administrators make higher salaries (faculty make more before 8.33
years and they will become equal in salary at approximately 8.33 years of
service). The regression equation for
faculty shows that the best estimate of starting salary for faculty is $15,000
(the intercept in the equation). For
every additional year of service, salary increases on average by $900 (the
slope). For administrative staff, the
best estimate of starting salary is $10,000 (the intercept), but every year of
additional service increases the salary by an average of $1500 (the slope).

1. R-squared
(r_{}) is also known as the coefficient of determination. R_{} allows you to determine the amount of variation in the
criterion variable that can be explained by the predictor variable. The amount of variation that the predictor
variable accounts for is obviously an indicator of how strong a predictor that
variable is. However, it is important to
note that r_{} does not indicate a causal link between the predictor and
the criterion variables. Yet, r_{} may provide more information as to whether the predictor variable
is a strong predictor and, if so, how strong a predictor it is. R_{} may also allow you to determine which variables are best
suited to be included in a model (or, at least, the adjusted r_{} value can).

2. The
pros of such a study include the fact that the high positive correlation
(r=.80) between BAC and accidents indicates the two variables are strongly
related and supports the researcher’s hypothesis. The N is rather large, which is a pro. Additionally, the r_{} is .64, so 64% of the variation in accidents can be
explained by blood alcohol content.
However, the main con about the apparent goal of this study is that the
researcher is trying to establish a causal link on the basis of a correlational study (and correlation does not equal
causation). Therefore, the researcher,
while clearly demonstrating a strong relation between alcohol and accidents,
cannot conclude that alcohol causes accidents, despite the large
correlation.