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HI6007 Statistics

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HI6007 Statistics

0 Download3 Pages / 610 Words

Course Code: HI6007
University: Holmes Institute

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Country: Australia

Question:

Question 1
Below you are given the examination scores of 20 students (data set also provided in accompanying MS Excel file).
Construct a frequency distribution, cumulative frequency distribution, relative frequency distribution, cumulative relative frequency distribution and percent frequency distribution for the data set using a class width of 10.
 
Construct a histogram showing the percent frequency distribution of the examination scores. Comment on the shape of the distribution.
Question 2
Shown below is a portion of a computer output for a regression analysis relating supply (Y in thousands of units) and unit price (X in thousands of dollars).

What has been the sample size for this problem?
Determine whether or not supply and unit price are related. Use α = 0.05. Determine whether or not demand and unit price are related. Use α = 0.05.

c.Compute the coefficient of determination and fully interpret its meaning. Be very specific.
d.Compute the coefficient of correlation and explain the relationship between supply and unit price.

Predict the supply (in units) when the unit price is $50,000.

A company has recorded data on the weekly sales for its product (y), the unit price of the competitor’s product (x1), and advertising expenditures (x2). The data resulting from arandom sample of 7 weeks follows. Use Excel’s Regression Tool to answer the following questions (data set also provided in accompanying MS Excel file). Week Price Advertising Sales

What is the estimated regression equation? Show the regression output.
Determine whether the model is significant overall. Use α = 0.10.
Determine if competitor’s price and advertising is individually significantly related to sales. Use α = 0.10.

Based on your answer to part (c), drop any insignificant independent variable(s) and re-estimate the model. What is the new estimated regression equation?  Interpret the slope coefficient(s) of the model from part (d).

Answer:

Question 1

The frequency distribution
Histogram (exam score)

The histogram shape represents that distribution of exam scores is not-normal as there is significant deviation and also the presence of skew. The curve is also not follows a perfect bell shape curve which is indicative of the normal distribution (Hair, et.al., 2015).
Question 2
Supply (y) is dependent variable because it depends on the unit price of product and hence, unit price (x) is independent variable.
ANOVA TABLE

Sample size is computed based on the degree of freedom
Hypothesis testing

Hypotheses for significance of slope coefficient
Unit price: Slope coefficient 0.029, Standard error 0.021
Degree of freedom =sample size – 2 = 39
Hypothesis testing: Two tailed
  = 0.05
p value > 0.05 i.e. 0.175 >> 0.05
Hence, cannot reject null hypotheses because p is greater than alpha (significance level). Therefore, slope is insignificant and thus, supply and unit price of the product is not related.

“Coefficient of determination”

ANOVA TABLE
Coefficient of determination is indicative of the model and the value comes out to be quite low and the model is not statistically good fit model. Further, the value indicates that mere 4.8% of deviations in the supply will be explained by deviation in unit prices.

“Coefficient of correlation”

Select positive value of R
The unit price slope coefficient comes out to be positive and therefore, the sign of the R will also be selected as +0.219. The value is indicative that intensity of the association between unit price and supply is quite weak (Hair, et.al., 2015).

Supply for unit price of product $50,000 need to be found.

Regression equation
Hence, supply for unit price of product $50,000 is 55526 units.
Question 3
ANOVA TABLE
Hypothesis testing
Hypotheses
Test statistic (F value) from ANOVA table: 6.14.
Alpha = 0.05
The p value (highlighted) = 0.006,
(0.05>>0.006) (Alpha>> p value)
Hence, reject null hypotheses because p is lower than alpha (significance level). Therefore, alternative hypothesis is accepted and final conclusion would be made that “at least one group mean is not equal (Flick, 2015).”
Question 4

Regression output  

In present case, sale is dependent variable which depends on price and advertising expenditure which are independent variables.
Linear regression equation

Hypothesis testing to check the significance of the model.

Alpha = 0.10
The significance F (highlighted) = 0.0526
(0.01>>0.0526) (Alpha>>significance F)
Hence, reject null hypotheses because p is lower than alpha (significance level). Therefore, alternative hypothesis is accepted and final conclusion would be made that “model is significance (Eriksson and Kovalainen).”

Hypothesis testing to check the whether the slope is significant or not in context of sales.

Price and Sales

Advertising and Sales

Hypotheses

Hypotheses

Alpha = 0.1

Alpha = 0.1

Corresponding p value = 0.036

Corresponding p value =  0.970

The alpha is higher than p value

The alpha is not higher than p value

Reject null hypothesis and accept alternative hypothesis

Fails to reject null hypothesis and cannot accept the alternative hypothesis

Price is significant of the sale of product.

Advertising expenditure is insignificant of the sale of product.

As per above discussion, the insignificant variable is advertising and hence, would be eliminated for the new model.

New regression output
Linear Regression equation

“Slope coefficient (price) is 41.60 which imply that when the price is increased by $1 then the respective sales will also rise by 41.60 units (Eriksson and Kovalainen).”

Reference
Eriksson, P. and Kovalainen, A. (2015) Quantitative methods in business research. 3rd ed. London: Sage Publications.
Flick, U. (2015) Introducing research methodology: A beginner’s guide to doing a research project. 4th ed. New York: Sage Publications.
Hair, J. F., Wolfinbarger, M., Money, A. H., Samouel, P., and Page, M. J. (2015) Essentials of business research methods. 2nd ed. New York: Routledge.

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