Statistics: regression model and hypothetical tests
- Identify the steps in interpreting a regression model. Interpret the following data:
Y = 5.0 + .30X1 where the dependent variable equals turnover intentions for line managers and the
independent variable equals the number of employees supervised
Y = 250 � 4.0X1 where the dependent variable is the number of hits on a new banner ad and the
independent variable is the number of weeks the ad has run
The answer must be in 75 words or more.Go to page 549 in your textbook and offer a thorough
interpretation of question
2Using Case Exhibit 21.1-1 on page 527 in the textbook, please calculate the mean average miles per
gallon. Compute the sample variance and sample standard deviation. Determine the most appropriate
statistical test using the 0.5 significance level. Provide your findings in the space provided.
Your response should be at least 75 words in length. You are required to use at least your textbook as
source material for your response. All sources used, including the textbook, must be referenced;
paraphrased and quoted material must have accompanying citations.
Statistics: regression model and hypothetical tests 2
- Interpret the computer cross-tab output, including a Chi-square test. Variable COMMUTE is �How did
you get to work last week?� Variable GENDER is �Are you male or female?� Comment on the
appropriateness of the statistical test used (make sure that your response includes information on the
types of variables used and the scales of measurement). Describe an alternative approach that may be
used.
3Your response should be at least 200 words in length. You are required to use at least your textbook
as source material for your response. All sources used, including the textbook, must be referenced;
paraphrased and quoted material must have accompanying citations
Statistics: regression model and hypothetical tests
Statistics: regression model and hypothetical tests 3
A linear model is of the form Y=b 0 +b 1 X+ε the constant b 0 is known as the intercept and
the coefficient is known as the parameter estimate for the variable X and ε is the error term.
From the above equations it means that upon plotting the regression model on an X-Y graph, the
line will be straight and it intercepts the y-axis at point 5 and the estimate parameter is 30.On the
second model the y-intercept is 250 and the estimating parameter for the dependable variable is
minus four. Therefore from the first model the line managers are estimated by a factor of 30
while in the second model the number of hits in the new banner is negative four. The number of
weeks is 250 from the second model and the number of employees supervised in the first model
is equal to 5.
Interpretation
From the first equation the dependent variable represents the line manager turnover and
the independent variable is the number of employees supervised. This means that if the number
of employees to be supervised increases by one then the line manager turnover will increase a
factor of .30.
From the second equation the dependent variable represents the number of hits on the
banner and the independent variable represents the number of weeks. This means that if the
number of weeks increases by 1 then the hits on the banner will reduce by a factor of 4 (four)
Question 2
Hypothesis
(a) The null hypothesis
Statistics: regression model and hypothetical tests 4
H 0 : µ=µ 0 =30
Alternatives
H 0 : µ≠30 (two-sided)
H 1 : µ˃30 (one-sided to right)
H 1 : µ˂30 (on- sided to left)
(b) Data
30.9,24.5,31.2,28.7,35.1,29.0,28.8,23.1,31.0,30.2,28.4,29.3,27.0,26.7,31.0,23.5,29.4,26.3,27.5,28
.2,28.4,29.1,21.9,30.9
Mean=680.1/24=28.3375
Variance= (30.9-28.3375) 2 +(24.5-28.3375) 2 +(31.2-28.3375) 2 +(28.7-28.3375) 2 +(35.1-
28.3375) 2 +(29-28.3375) 2 +(28.8-28.3375) 2 +(23.1-28.3375) 2 +(31-28.3375) 2 +(30.2-
28.3375) 2 +(28.4-28.3375) 2 +(29.3-28.3375) 2 +(27-28.3375) 2 +(26.7-28.3375) 2 +(31-
28.3375) 2 +(23.5-28.3375) 2 +(29.4-28.3375) 2 +(26.3-28.3375) 2 +(27.5-28.3375) 2 +(28.2-
28.3375) 2 +(28.4-28.3375) 2 +(29.1-28.3375) 2 +(21.9-28.3375) 2 +(30.9-28.3375) 2
=6.5664+14.7264+8.1939+0.131406+45.73141+0.4389+0.2139+27.4314+7.0889+3.4689+0.003
906+0.9264+1.7889+2.6814+7.0889+23.4014+1.1289+4.1514+0.7014+0.0189+0.00390
6+0.5814+41.4414+6.5664
Variance =204.476128/ (24-1)=204.476128/23=8.89027
Standard deviation = sqrt (8.89027) = 2.9817
(c)
T stat = (28.3375-30)/(2.9817/√(24))=-1.6625/0.608634=-2.7315267
Statistics: regression model and hypothetical tests 5
Z=-2.7315267, from the z-test table α=0.0033.This is less than the level of significance
which is 0.5
The null hypothesis is rejected since the t stat is negative. Therefore, the average is not 30
gallons per kilometer but instead it is less than 30.
(3)
The computer calculates the chi-square value. The chi-square value is a single
number which adds up all the differences between the actual data and the data expected if
there is no difference. If the expected and the actual data are identical meaning that there
is no difference then the chi-square value outputted by the computer is zero. If the
difference is big then the computer will output a bigger chi-square value.
Interpretation
If there is a greater difference between the actual and the expected data a larger
chi-square value will be produced. Larger chi-square value means that there is greater
probability that there is a significant difference between the number of males or females
who used a particular means to commute to work.
If the chi-square value is found to be greater or equal to the critical value there is
a significant difference between the males and females and the conclusion is that the
sample studied supports the hypothesis of a difference.
If the chi-square value computed is found to be less than the critical value then there is no
significant difference between the males or females who used a particular means to
commute to work. The conclusion is that the sample does not support the hypothesis of a
difference (anderson, 2010) .
Statistics: regression model and hypothetical tests 6
The alternative for chi-square test is Fisher’s Exact Test. The problem being
investigated is a 2*2 table and the chi-square test will control the false positives to the
desired threshold as long as the expected value of each cell of the table is found to be
greater than 5.
Work cited
anderson. (2010). statistics for business and economics. New-york: south-westorn cengage
learning.
