Beachcomber Ltd in a local car dealership that sells used and new vehicles. The manager of the company wants to know how different variables affect the sales of his vehicles. A random sample of yearly data was taken with the view to testing the model: SALĖS=a+BAGE+YMIL+8ENG Where SALES= amount that a vehicle is sold for($000's), AGE = age of the vehicle, MIlIL= the total mileage of the vehicle at the point of sale and ENG = the size of the engine. The sample of data was processed using MINITAB and the following is an extract of the output obtained: The regression equation is ***** Predictor Coef StDev t-ratio p-value Constant 1.7586 0.2525 6.9648 0.0000 AGE 0.2124 0.3175 0.5042 MIL -0.7527 0.3586 -2.0991 ENG 4.8124 0.6196 7.7664 0.0000 Analysis of Variance Source DF s MS Regression Error 3 413.1291 138.7097 *** 0.00 50 457.7607 2.2888 Total 53 a) What is dependent and independent variables? b) Fully write out the regression equation c) Fill in the missing values ***, ***, and “ d) Hence test whether 8 is significant. Give reasons for your answer. e) Perform the F Test making sure to state the null and alternative hypothesis. f) Given an interpretation of the term "R-sq" and comment on its value.
Beachcomber Ltd in a local car dealership that sells used and new vehicles. The manager of the company wants to know how different variables affect the sales of his vehicles. A random sample of yearly data was taken with the view to testing the model: SALĖS=a+BAGE+YMIL+8ENG Where SALES= amount that a vehicle is sold for($000's), AGE = age of the vehicle, MIlIL= the total mileage of the vehicle at the point of sale and ENG = the size of the engine. The sample of data was processed using MINITAB and the following is an extract of the output obtained: The regression equation is ***** Predictor Coef StDev t-ratio p-value Constant 1.7586 0.2525 6.9648 0.0000 AGE 0.2124 0.3175 0.5042 MIL -0.7527 0.3586 -2.0991 ENG 4.8124 0.6196 7.7664 0.0000 Analysis of Variance Source DF s MS Regression Error 3 413.1291 138.7097 *** 0.00 50 457.7607 2.2888 Total 53 a) What is dependent and independent variables? b) Fully write out the regression equation c) Fill in the missing values ***, ***, and “ d) Hence test whether 8 is significant. Give reasons for your answer. e) Perform the F Test making sure to state the null and alternative hypothesis. f) Given an interpretation of the term "R-sq" and comment on its value.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.4: Discrete Random Variables; Applications To Decision Making
Problem 27E
Related questions
Concept explainers
Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
Question
Answer from D to F
Also, please use the Statistical tables provided
![Probability
Poisson distribution
P(A or B) = P(A) + P(B) – P(A and B)
P(A and B) = P(A) x P(B) for independent events
X- Po(A)
P(A and B) = P(A) x P(B|A) for dependent events
P(X - x) = **
x!
P(A and B)
P(B|A) =
P(A)
Confidence Interval
Normal Distribution
1. z-confidence
interval:
X- N(4, ơ)
X-u
2. t-confidence
interval:
1. Standard normal: Z -
(df -n-1)
3. Confidence interval
for proportion:
P(1 – P)
n
Sampling Distribution
1. 4 =4
2.
Test Statistics
X-4
1. z-test for p : 2=
3.
X - µ
2.
t-test for u: t =
(d.f. = n-1)
S/ Vn
Discrete Probability Distribution
3. z-test forp: z-
» np 2 5
1. EÇX) = µ, = Ex,P,
P(1 - P),
and np z 5 (where q = 1-p)
Var(X) = o = 2(x, -4,)°p,
%3D
%3D
4. Chi-square test statistic = y0- E)
(0-E)
Binomial Distribution
Σ
X- Bin(n, p)
n-k
P(X - k) -
P" (1-
n!
p (1-
n-k
k!(n -k)!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F86f2537f-9d29-4c47-890a-b5c900cb85d5%2F2dd23479-e51e-4a29-ad5a-26cb0bd7f17d%2F0scrga_processed.png&w=3840&q=75)
Transcribed Image Text:Probability
Poisson distribution
P(A or B) = P(A) + P(B) – P(A and B)
P(A and B) = P(A) x P(B) for independent events
X- Po(A)
P(A and B) = P(A) x P(B|A) for dependent events
P(X - x) = **
x!
P(A and B)
P(B|A) =
P(A)
Confidence Interval
Normal Distribution
1. z-confidence
interval:
X- N(4, ơ)
X-u
2. t-confidence
interval:
1. Standard normal: Z -
(df -n-1)
3. Confidence interval
for proportion:
P(1 – P)
n
Sampling Distribution
1. 4 =4
2.
Test Statistics
X-4
1. z-test for p : 2=
3.
X - µ
2.
t-test for u: t =
(d.f. = n-1)
S/ Vn
Discrete Probability Distribution
3. z-test forp: z-
» np 2 5
1. EÇX) = µ, = Ex,P,
P(1 - P),
and np z 5 (where q = 1-p)
Var(X) = o = 2(x, -4,)°p,
%3D
%3D
4. Chi-square test statistic = y0- E)
(0-E)
Binomial Distribution
Σ
X- Bin(n, p)
n-k
P(X - k) -
P" (1-
n!
p (1-
n-k
k!(n -k)!
![Question 4
Beachcomber Ltd in a local car dealership that sells used and new vehicles. The manager of the
company wants to know how different variables affect the sales of his vehicles. A random sample of
yearly data was taken with the view to testing the model:
SALĖS-a+BAGE+YMIL+8ENG
Where SALES= amount that a vehicle is sold for($000's), AGE = age of the vehicle, MIL= the total
mileage of the vehicle at the point of sale and ENG = the size of the engine. The sample of data was
processed using MINITAB and the following is an extract of the output obtained:
The regression equation is *****
Predictor
Coef
StDev
t-ratio
p-value
Constant
1.7586
0.2525
6.9648
0.0000
AGE
0.2124
0.3175
0.5042
MIL
-0.7527
0.3586
-2.0991
ENG
4.8124
0.6196
7.7664
0.0000
Analysis of Variance
Source
DF
MS
F
Regression
3
413.1291
138.7097
+**
0.00
Error
50
457.7607
2.2888
Total
53
a) What is dependent and independent variables?
b) Fully write out the regression equation
c) Fill in the missing values ***, ****, and **
d) Hence test whether 8 is significant. Give reasons for your answer.
e) Perform the F Test making sure to state the null and alternative hypothesis.
f) Given an interpretation of the term "R-sq" and comment on its value.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F86f2537f-9d29-4c47-890a-b5c900cb85d5%2F2dd23479-e51e-4a29-ad5a-26cb0bd7f17d%2F4a7i5n_processed.png&w=3840&q=75)
Transcribed Image Text:Question 4
Beachcomber Ltd in a local car dealership that sells used and new vehicles. The manager of the
company wants to know how different variables affect the sales of his vehicles. A random sample of
yearly data was taken with the view to testing the model:
SALĖS-a+BAGE+YMIL+8ENG
Where SALES= amount that a vehicle is sold for($000's), AGE = age of the vehicle, MIL= the total
mileage of the vehicle at the point of sale and ENG = the size of the engine. The sample of data was
processed using MINITAB and the following is an extract of the output obtained:
The regression equation is *****
Predictor
Coef
StDev
t-ratio
p-value
Constant
1.7586
0.2525
6.9648
0.0000
AGE
0.2124
0.3175
0.5042
MIL
-0.7527
0.3586
-2.0991
ENG
4.8124
0.6196
7.7664
0.0000
Analysis of Variance
Source
DF
MS
F
Regression
3
413.1291
138.7097
+**
0.00
Error
50
457.7607
2.2888
Total
53
a) What is dependent and independent variables?
b) Fully write out the regression equation
c) Fill in the missing values ***, ****, and **
d) Hence test whether 8 is significant. Give reasons for your answer.
e) Perform the F Test making sure to state the null and alternative hypothesis.
f) Given an interpretation of the term "R-sq" and comment on its value.
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