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.