Please assist me with help in Statistics by anwersing the following
practice problems for me. Thank you for your help!
6.
4. Cellulon, a manufacturer of a new type of home insulation, wants to
develop guidelines for
builders and consumers regarding the effects on natural gas
consumption (1) of the thickness
of the insulation in the attic of a home and (2) of the outdoor
temperature. In the laboratory
they varied the insulation thickness and temperature. A few of the findings are:
Monthly Gas Consumption Thickness of r Insulation Outdoor Temperature
(cubic feet), (inches), (°F),
Y X1 X2
30.3 6 40
26.9 12 40
22.1 8 49
Based on the sample results, the regression equation is:
Y1=62.65 ? 1.86X1 - 0.52X2
a. How much natural gas can homeowners expect to use per month if they
install 6 inches
of insulation and the outdoor temperature is 40 degrees F?
b. What effect would installing 7 inches of insulation instead of 6
have on the monthly natural
gas consumption (assuming the outdoor temperature remains at 40 degrees F)?
c. Why are the regression coefficients b1 and b2 negative? Is this logical?
7.
16. Mike Wilde is president of the teachers? union for Otsego School
District. In preparing for
upcoming negotiations, he would like to investigate the salary
structure of classroom teachers
in the district. He believes there are three factors that affect a
teacher?s salary: years
of experience, a rating of teaching effectiveness given by the
principal, and whether
the teacher has a master?s degree. A random sample of 20 teachers
resulted in the following
data.
Salary Years of Principal?s Master?s
($ thousands), Experience, Rating, Degree,*
Y X1 X2 Y3
21.1 8 35 0
23.6 5 43 0
19.3 2 51 1
33.0 15 60 1
28.6 11 73 0
35.0 14 80 1
32.0 9 76 0
26.8 7 54 1
38.6 22 55 1
21.7 3 90 1
15.7 1 30 0
20.6 5 44 0
41.8 23 84 1
36.7 17 76 0
28.4 12 68 1
23.6 14 25 0
31.8 8 90 1
20.7 4 62 0
22.8 2 80 1
32.8 8 72 0
*1 =yes, 0 =no.
a. Develop a correlation matrix. Which independent variable has the
strongest correlation with the dependent variable? Does it appear
there will be any problems with
multicollinearity?16. a. Years. No.
b. Determine the regression equation. What salary would you estimate
for a teacher with
five years? experience, a rating by the principal of 60, and no
master?s degree?b. Y_ _ $23,655
c. Conduct a global test of hypothesis to determine whether any of the
net regression
coefficients differ from zero. Use the .05 significance level.c. F _ 52.72
d. Conduct a test of hypothesis for the individual regression
coefficients. Would you
consider deleting any of the independent variables? Use the .05
significance level.d. Drop X3.
e. If your conclusion in part (d) was to delete one or more
independent variables, run the
analysis again without those variables.
8.
17. The district sales manager for a major automobile manufacturer is
studying car sales.
Specifically, he would like to determine what factors affect the
number of cars sold at a
dealership. To investigate, he randomly selects 12 dealers. From these
dealers he obtains
the number of cars sold last month, the minutes of radio advertising
purchased last month,
the number of full-time salespeople employed in the dealership, and
whether the dealer is
located in the city. The information is as follows:
Cars Sold Advertising Sales City, Cars Sold Advertising Sales
Last Month, , Force, Last Month, Force, City,
Y X1 X2 X3 Y X1 X2 X3
127 18 10 Yes 161 25 14 Yes
138 15 15 No 180 26 17 Yes
159 22 14 Yes 102 15 7 No
144 23 12 Yes 163 24 16 Yes
139 17 12 No 106 18 10 No
128 16 12 Yes 149 25 11 Yes
a. Develop a correlation matrix. Which independent variable has the
strongest correlation
with the dependent variable? Does it appear there will be any problems with
multicollinearity?
b. Determine the regression equation. How many cars would you expect
to be sold by a
dealership employing 20 salespeople, purchasing 15 minutes of
advertising, and located
in a city?
c. Conduct a global test of hypothesis to determine whether any of the
net regression
coefficients differ from zero. Let _ .05.
d. Conduct a test of hypothesis for the individual regression
coefficients. Would you
consider deleting any of the independent variables? Let _ .05.
e. If your conclusion in part (d) was to delete one or more
independent variables, run the
analysis again without those variables.
9.
21. How important is GPA in determining the starting salary of recent
business school graduates?
Does graduating from a business school increase the starting salary?
The Director of
Undergraduate Studies at a major university wanted to study these
questions. She gathered
the following sample information on 15 graduates last spring to investigate these
questions.
Student Salary GPA Business
1 $31.5 3.245 0
2 33.0 3.278 0
3 34.1 3.520 1
4 35.4 3.740 1
5 34.2 3.520 1
6 34.0 3.421 1
7 34.5 3.410 1
8 35.0 3.630 1
9 34.7 3.355 1
10 32.5 3.080 0
11 31.5 3.025 0
12 32.2 3.146 0
13 34.0 3.465 1
14 32.8 3.245 0
15 31.8 3.025 0
The salary is reported in $000, GPA on the traditional 4-point scale.
A 1 indicates the student
graduated from a school of business; a 0 indicates that the student graduated from
one of the other schools.
a. Develop a correlation matrix. Do you see any problems with multicollinearity?
b. Determine the regression equation. Discuss the regression equation.
How much does
graduating from a college of business add to a starting salary? What
starting salary
would you estimate for a student with a GPA of 3.00 who graduated from a college of
business?
c. What is the value of R2? Can we conclude that this value is greater than 0?
d. Would you consider deleting either of the independent variables?
10.
22. A mortgage department of a large bank is studying its recent
loans. Of particular interest is
how such factors as the value of the home (in thousands of dollars),
education level of the
head of the household, age of the head of the household, current
monthly mortgage payment
(in dollars), and sex of the head of the household (male _ 1, female _
0) relate to the
family income. Are these variables effective predictors of the income
of the household?
A random sample of 25 recent loans is obtained.
Income Value Years of Education Age Mortgage Payment Sex
($ thousands) ($ thousands)
$40.3 $190 14 53 $230 1
39.6 121 15 49 370 1
40.8 161 14 44 397 1
40.3 161 14 39 181 1
40.0 179 14 53 378 0
38.1 99 14 46 304 0
40.4 114 15 42 285 1
40.7 202 14 49 551 0
40.8 184 13 37 370 0
37.1 90 14 43 135 0
39.9 181 14 48 332 1
40.4 143 15 54 217 1
38.0 132 14 44 490 0
39.0 127 14 37 220 0
39.5 153 14 50 270 1
40.6 145 14 50 279 1
40.3 174 15 52 329 1
40.1 177 15 47 274 0
41.7 188 15 49 433 1
40.1 153 15 53 333 1
40.6 150 16 58 148 0
40.4 173 13 42 390 1
40.9 163 14 46 142 1
40.1 150 15 50 343 0
38.5 139 14 45 373 0
a. Determine the regression equation.
b. What is the value of R2? Comment on the value.
c. Conduct a global hypothesis test to determine whether any of the
independent variables
are different from zero.
d. Conduct individual hypothesis tests to determine whether any of the
independent variables
can be dropped.
e. If variables are dropped, recompute the regression equation and R2. |
