a) What is dependent and independent variables? b) Fully write out the regression equation c) Fill in the missing values **', ***, and

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 26PPS
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Answer from A to C

 

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)!
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.
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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