Statistics-The usualobjective of regression analysis is to predict estimate

Name:

ID: ___________

v There are 4 parts: Part A: True/ False (1-20) Part B: Select the correct answer for the following questions (21-40) Part C: Work Problem (41-52) **All work in part C must be shown step by step** v Two different ways to submit your answer sheet 1. Scan your answer sheet and place it in ONE FILEat drop-box. (preferable) Use MS-Word and place it in a drop-box. v **Excel is not acceptable for this test v **Deadline:Monday, December 7, 2015 by noon (CST) v **All work in part C must be shown step by step in order to receive credit

Online Final
Exam

Part
A: True/ False (1-20)

___T___ 1.
The usualobjective of
regression analysis is to predict estimate the value of one variable when the
value of another variable is known.

___T___ 2.
Correlation analysis is concerned with measuring the strength of the
relationship between two variables.

___F___ 3.
The term e_i in the simple linear regression model indicates the
amount of change in Y for a unit change in X.

___T___ 4.
In the sample regression equation y = a + bx, b is the slope of the regression
line.

___F___ 5.
The coefficient of determination can assume any value between -1 and +1.

___F___ 6.
In the least squares model, the explained sum of squares is always smaller than
the regression sum of squares.

___T___ 7.
The sample correlation coefficient and the sample slope will always have the
same sign.

___F___ 8.
Given the sample regression equation y = -3 + 5x, we know that in the sample X
and Y are inversely related.

___F___ 9.
Given the sample regression equation y = 5 – 6x, we know that when X = 2, Y =
17.

___T___ 10.
An important relationship in regression analysis is
=
.

___T___ 11.
Regression analysis is concerned with the form of the relationship among
variables, whereas correlation analysis is conc erned
with the strength of the relationship.

___F___ 12.
The correlation coefficient indicates the amount of change in Y when X change
by one unit.

___T___ 13.
In simple linear regression analysis, when the slope is equal to zero, the
independent variable does not explain any of the variability in the dependent variable.

___T___ 14.
One of the purposes of regression analysis is to estimate a mean of the
independent variable for given values of the dependent variable.

___T___ 15.
The variable that can be manipulated by the investigator is called the
independent variable.

___T___ 16.
When b = 0, X and Y are not related.

___F___ 17.
If zero is contained in the 95% confidence interval for b, we may reject H_o:
b = 0 at the 0.05 level of significance.

___F___ 18.
If in a regression analysis the explained sum of squares is 75 and the
unexplained sum of square is 25, r² = 0.33.

___T___ 19.
In general, the smaller the dispersion of observed points about a fitted
regression line, the larger the value of the coefficient of determination.

___F___ 20.
When small values of Y tend to be paired with small values of X, the
relationship between X and Y is said to be inverse.

Part B:Select
the correct answer for the following questions (21 – 40)

___a___
21. The variable about which the investigator wishes to make predictions or
estimates is called the

a. dependent variable b. unit of
association

c. independent variable d. discrete
variable

___b___
22. In regression analysis, the quantity that gives the amount by which Y
changes for a unit change in X is called the

a. coefficient of determination b. slope of the regression line

c. Y intercept of the regression
line d. correlation
coefficient

___c___ 23. In the equation y = b₀ +b₁
(x), b₀ is the

a.
coefficient of determination b. slope of the
regression line

c. y intercept of the regression
line d.
correlation coefficient

___b___ 24. In the equation y = b₀ + b₁
(x), b₁ is the

a.
coefficient of determination b. slope of the regression line

c. y
intercept of the regression line d. correlation coefficient

___a___ 25. In regression and correlation analysis,
the measure whose values are restricted to the range 0 to 1, inclusive, is the

a. coefficient of determination b. slope of the
regression line

c. y
intercept of the regression line d. correlation coefficient

___d___ 26. In regression and correlation analysis,
the measure whose values are restricted to the range -1 to +1, inclusive, is
the

a.
coefficient of determination b. slope of the
regression line

c. y
intercept of the regression line d. correlation coefficient

___d___ 27. The quantity
is called the _______________ sum of
square.

a.
least
b. explained

c.
total
d. unexplained

___d___ 28. If, in the regression model,
= 0, we say there is _____________ linear
relationship between X and Y.

a. an
inverse
b. a significant

c. a
direct d. no

___a___ 29. If, in the regression model, b is
negative, we say there is _____________ linear relationship between X and Y.

a. an inverse
b. a significant

c. a
direct d.
no

___d___ 30. The _______________ sum of square is a
measure of the total variability in the observed values of Y that is accounted
for by the linear relationship between the observed values of X and Y.

a.
unexplained
b. total

c.
error
d. explained

___d___ 31. If two variables are not related, we know
that ________________.

a. their correlation
coefficient is equal to zero.

b. the
variability in one of them cannot be explained by the other.

c. the
slope of the regression line for the two variables is equal to zero.

d. all of the above statements
are true.

___b___ 32. In simple linear regression analysis, if
the correlation coefficient is equal to 1.0, ______________.

a. the
slope is equal to 1.0

b. all the variability in the
dependent variable is explained by the independent variable.

c. the y
intercept is equal to 1.0

d. the
relationship between the two variables can be described as a bivariable normal
distribution.

___d___ 33. The following results were obtained from a
simple linear regression analysis. Total sum of square = 5.7640. Unexplained
sum of square = 0.2225. The coefficient of determination is ____

a.
0.0402
b. 0.0386

c.
0.9805
d. 0.9614

___a___ 34. The following results were obtained as
part of a simple linear correlation analysis: Y = 97.98 – 4.33x regression sum
of squares = 2680. 27. Error sum of squares = 125.40. Total sum of squares =
2805.67. The sample correlation coefficient is ____

a. -0.9774
b. 0.9553

c.
0.2114
d. 0.0447

___d____ 35. The following equation describes the
relationship between output and labor input at a sample of work stations in a
manufacturing plant:
.
Suppose, for a selected workstation, the labor input is 5. The predicted output
is _____________.

a.
4.55
b. 2.35

c.
2.20
d. 13.35

___a___ 36. In regression and correlation analysis,
the entity on which sets of measurements are taken is called the
______________.

a. dependent variable b.
independent variable

c. variables d. discrete variable

___c___ 37. The quantity
is
called the _____________ sum of squares.

a.
least
b. total

c. explained
d. unexplained

___b___ 38. If, in the regression model,
is positive, we say there is ____________
linear relationship between X and Y.

a. an
inverse
b. a direct

c. a
significant
d. no

___b___ 39. If, as X increase, Y tends to increase, we
say there is ____________ linear relationship between X and Y.

a. an
inverse
b. a direct

c. a
significant
d. no

___d___ 40. The explained sum of squares divided by
the total sum of squares yield the _______.

a. F
statistic
b. total mean square

c. p
value
d. coefficient of multiple determination

Part
C: Work Problem (41-52)**All work in part C must be shown step by step**

41.
Work problem number 13 on page 8-11. (a-c)

a) 45-1.96*(5.8/√30)≤µ≤45+1.96*(5.8/√30) 45 – 2.078 ≤ µ ≤ 45 + 2.078 42.922 ≤ µ ≤ 47.078

b) 45-1.96*(5.8/√60)≤µ≤45+1.96*(5.8/√60) 45 – 1.468 ≤ µ ≤ 45 + 1.468 43.532 ≤ µ ≤ 46.468

c) 45-1.96*(5.8/√60)≤µ≤45+1.96*(5.8/√60) 45 – 1.198 ≤ µ ≤ 45 + 1.198 43.802 ≤ µ ≤ 46.198

42.
Use problem number 1 on page 9-18
to answer the following questions (a-e).

Consider the following hypothesis
test.

H_o: µ ≥ 10

H_a: µ < 10

A sample
with n = 50 provides a sample mean of 9.46 and sample standard deviation of 2.
At α = 0.05, what is the critical value for z or t? What is the
rejection rule?

a) Use Z or T test? And why? Use Z-test because sample size is >30. zcritical = -1.645	b) At α = 0.05, what is the rejection rule? 1. Reject Ho if 1. Computed |z| ≥ Table Value 2. α ≥ P value Reject Ho if z < -1.645
c) Compute the value of the test statistic.	d) What is the p-value? .5-.4719 = .0281
e) What is your conclusion? Since the test statistic is in the rejection region we reject the null hypothesis.

43.
Use problem number 13 on page 9-20 (a-h)

A bath soap manufacturing process is designed to produce a mean of
120 bars of soap per batch. Quantities over or under the standard are
undesirable. A sample of ten batches shows the following number of bar of soap.

108

118

120

122

119

113

124

122

120

123

Using a 0.05 level of significance, test to see whether the sample
results indicate that the manufacturing process is functioning properly

No.	x	x-squared	x-xbar	(x-xbar)squared
1	108	11664	-10.9	118.81
2	118	13924	-0.9	0.81
3	120	14400	1.1	1.21
4	122	14884	3.1	9.61
5	119	14161	0.1	0.01
6	113	12769	-5.9	34.81
7	124	15376	5.1	26.01
8	122	14884	3.1	9.61
9	120	14400	1.1	1.21
10	123	15129	4.1	16.81
Total	1189	141591	0	218.9

Sum = 1189
Mean (1189/10) = 118.9

Sample
Variance = 218.9/9 = 24.3222

Standard
Deviation = √24.3222 = 4.932

a) What is the sample mean (108+118+120+122+119+113+124+122+120+123)/11 Sum = 1189 Mean (1189/10) = 118.9 =118.9	b) What is the sample standard deviation Standard Deviation = √24.3222 =4.932
c) Use Z or T test? And why? Use t-test because sample size is ≤ 30	d) What is your hypothesis test Ho:µ = 118.9 Ha:µ>118.9
e) At α = 0.05, what is the rejection rule? Reject Ho if t < -2.262 or t > 2.262	f) Compute the value of the test statistic.
g) What is the p-value? .5-.4881 = .0119	h) What is your conclusion? Since the test statistic is not in the rejection region, we can not reject Ho. We don’t have sufficient evidence to conclude that the process is out of control.

44.
For n=6 data point, the following quantities have been calculated.

∑xy = 400

∑x = 40

∑y = 76

∑x2 = 346

∑y2 = 1160

a)Find	b)Find
c)Write the equation	d)Find
e)Find SST	f)Find
g) Construct the 95% confidence interval for the mean of y when x = 7	h)Construct the 95% confidence interval for the individual value of y when x = 9

45. The following data was collected
which yielded the regression equation: (see the printout)

A regression model relating plane
travelling. Given X, number of fuel consumed (in gallon) and Y, flying time
(1,000 mile) has been developed.

Given data
Flying Time (y)	27.9	25.2	23.8	23.4	23.4	22.2	22
Fuel Consumed (x)	276.5	251.2	235.1	248.8	249.4	242	239.8

The computer output from a regression
analysis of the data follows. Please fill in the blank and answer the following
questions (a-d).

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.877		ANOVA
R Square	0.768			df	SS	MS	F	Significance F
Adjusted R Square	-1.4		Regression	1	18.937	18.937	16.577	0.010
Standard Error	1.069		Residual	5	5.712	1.142
Observations	1		Total	6	24.649
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-8.859	8.077	-1.097	0.323	-29.621	11.904	-29.621	11.904
Fuel Consumed (x)	0.132	0.032	4.071	0.010	.049	0.215	0.049	.215

a) Write the estimated regression equation y = 5.824x + 109.285	b) What is the number of observations 1
c) Compute the F statistic and test the significance of the relationship at a .05 level of significance. F=16.577 Ho1: B1=0 and Ho2: B2=0	d) Predict the flying time when the plane consumed 270 Gallons of gas 270=5.824x + 109.285 270-109.285 = 5.824x 160.715=5.824x 160.715/5.824=x x=27.595 minutes travel time when 270 gallons of gas is consumed.

1. The following regression equation was
   obtained using the five independent variables.

Given that

a)	What percent of the variation is explained by the regression equation?	b)	What is the standard error of regression?
	99.4%		1.507
c)	What is the critical value of the F-statistic?	d)	What sample size is used in the print out?
	6.256		10
e)	What is the variance of the slope coefficient of income?
0.043852 = 0.001923
f)	Conduct a global test of hypothesis to determine if any of the regression coefficients are not zero.
Ho: β1 = β2 = β3 = β4 = β5 = 0 Ha: At least one of the coefficients is different than zero Because the test statistic (140.36) is greater than the critical value (6.256) we reject the null hypothesis. We have sufficient evidence to conclude that at least one of the regression coefficients is different than zero.
g)	Conduct a test of hypothesis on each of the independent variables. Would you consider eliminating outlets and bosses? Seeing the p-values for each independent variable, outlets, bosses, and age are not significant at a level of 0.05. So they can be eliminated from the model.

1. State whether
   should be accepted or rejected for
   ,
   given the following;
   (fill in the blank and circle your
   decision)

a)
= 2.34; df = 2 and 11

Computed F	Critical F	Decision
________	________	Reject / Fail to reject

b)
= 2.52; df = 4 and 20

Computed F	Critical F	Decision
________	________	Reject / Fail to reject

c)
= 4.29; df = 3 and 24

Computed F	Critical F	Decision
________	________	Reject / Fail to reject

1. Given the following, complete the
   ANOVA table and make the correct inference.

Source	SS	df	MS	F
Treatments	_____	2	3.24	_____
Error	_____	17	_____
Total	40.98	_____
		ANSWER
a)	What is your hypothesis?
b)	In the above ANOVA table, is the factor significant at 5% level of significant?
c)	What is the number of observations?

1. Given the following, complete the
   ANOVA table and make the correct inference.

Source	SS	df	MS	F
Treatments	_____	2	24.9	_____
Error	22.9	_____	_____
Total	_____	29
	ANSWER
a) What is your hypothesis?
b)In the above ANOVA table, is the factor significant at 5% level of significant?
c)What is the number of observations?

1. Given
   the following, complete the ANOVA table and make the correct inference.

Source	SS	df	MS	F
Treatments	_____	3	_____	_____
Error	1156.56	_____	_____
Total	2202	23
	ANSWER
a)What is your hypothesis?
b)In the above ANOVA table, is the factor significant at 5% level of significant?
c)What is the number of observations?

51. Use problem 4 on page 15-9 to answer
the following questions. (a-d)

A large hotel purchased 200 new
color televisions several months ago: 80 of one brand and 60 of each of two
other brands. Records were kept for each
set as to how many service calls were required, resulting in the table that
follows.

Number of service calls	Tv brand	Tv brand	Tv brand	Total
None	8	15	18	41
One	30	55	12	97
Two or more	22	10	30	62
Total	60	80	60	200

Assume the TV sets are random
samples of their brands. With 5% risk of
Type I error, test for an associatoni between TV brand and the number of
service calls.

a) Is the value
significant at 5% level of significance?

b) Write the
conclusion for this question

c) What is you hypothesis testing

d) What is your χ2?

c) Is the χ2 value significant at 5% level of significance?

d) Write the conclusion for this question.

52. An ad agency
asks each member of a random sample of 60 viewers to indicate which of six
television programs he or she prefers. Let

Program	1	2	3	4	5	6	Total
Number	5	8	10	12	12	13	60

e) What is you hypothesis testing

f) What is your χ2?

c) Is the χ2 value significant at 5% level of significance?

d) Write the conclusion for this question.