Question 1
Below you are given the examination scores of 20 students (data set also provided in accompanying MS Excel file).
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.
Compute the coefficient of determination and fully interpret its meaning. Be very specific.
 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.
Question 3
Allied Corporation wants to increase the productivity of its line workers. Four different programs have been suggested to help increase productivity. Twenty employees, making up a sample, have been randomly assigned to one of the four programs and their output for a day's work has been recorded. You are given the results below (data set also provided in accompanying MS Excel file).
 Construct an ANOVA table.
 As the statistical consultant to Allied, what would you advise them? Use a .05 level of significance.
Question 4
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 a random sample of 7 weeks follows. Use Excel's Regression Tool to answer the following questions (data set also provided in accompanying MS Excel file).
 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 reestimate the model. What is the new estimated regression equation? Interpret the slope coefficient(s) of the model from part (d).
Answer:
Below you are given the examination scores of 20 students (data set also provided in accompanying MS Excel file).
Answer
Class 
Frequency 
Cumulative frequency 
Relative frequency 
Cumulative relative frequency 
Percent frequency 
5059 
3 
3 
0.15 
0.15 
15% 
6069 
2 
5 
0.1 
0.25 
25% 
7079 
5 
10 
0.25 
0.5 
50% 
8089 
4 
14 
0.2 
0.7 
70% 
9099 
6 
20 
0.3 
1 
100% 
 Construct a histogram showing the percent frequency distribution of the examination Comment on the shape of the distribution. (2 marks)
The shape of the histogram shows a kind of left skewed distribution, this shows that the distribution is negatively skewed. However, the skewness is not severe.
Question 2 (8 marks)
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? (1 mark)
Sample size = 39+1+1 = 41
 Determine whether or not supply and unit price are related. Use α = 0.05. (2 marks)
We obtain the tvalue
The tcritical value is 2.022; this value is greater than the computed value hence the null hypothesis is not rejected. This means that supply and unit price are not related at α = 0.05.
 Compute the coefficient of determination and fully interpret its meaning. Be very specific. (2 marks)
The coefficient of determination is 0.048; this implies that unit price only explains 4.8% of the variation in the dependent variable
 Compute the coefficient of correlation and explain the relationship between supply and unit price. (2 marks)
The coefficient of correlation is 0.21921; this indicates that there is a weak positive relationship between supply and unit price.
 Predict the supply (in units) when the unit price is $50,000. (1 mark)
The regression equation model is;
Thus the supply is approximately 1505.
Question 3 (6 marks)
Allied Corporation wants to increase the productivity of its line workers. Four different programs have been suggested to help increase productivity. Twenty employees, making up a sample, have been randomly assigned to one of the four programs and their output for a day's work has been recorded. You are given the results below (data set also provided in accompanying MS Excel file).
 Construct an ANOVA table. (3 marks)
Answer
The following is the ANOVA Table
Anova: Single Factor 









SUMMARY 




Groups 
Count 
Sum 
Average 
Variance 
Program A 
5 
725 
145 
525 
Program B 
5 
675 
135 
425 
Program C 
5 
950 
190 
312.5 
Program D 
5 
750 
150 
637.5 
ANOVA 






Source of Variation 
SS 
df 
MS 
F 
Pvalue 
F crit 
Between Groups 
8750 
3 
2916.667 
6.140351 
0.00557 
3.238872 
Within Groups 
7600 
16 
475 










Total 
16350 
19 




 As the statistical consultant to Allied, what would you advise them? Use a .05 level of significance. (3 marks)
Answer
Looking at the above results, it can be seen that the pvalue is 0.00557 (a value less than α = 0.05). With this, we therefore reject the null hypothesis and conclude that the productivity varies based on the program. Results further showed that Program D had significantly higher productivity than any other program. As the statistical consultant to Allied, I would advise them to consider program D since more productivity would be realized from this program.
Question 4 (9 marks)
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 a random sample of 7 weeks follows. Use Excel's Regression Tool to answer the following questions (data set also provided in accompanying MS Excel file).
 What is the estimated regression equation? Show the regression output. (2 marks)
Answer
SUMMARY OUTPUT 



Regression Statistics 

Multiple R 
0.877814 
R Square 
0.770558 
Adjusted R Square 
0.655837 
Standard Error 
1.83741 
Observations 
7 

Coefficients 
Standard Error 
t Stat 
Pvalue 
Lower 95% 
Upper 95% 
Intercept 
3.597615 
4.052244 
0.887808 
0.424805 
7.65322 
14.84845 
Price 
41.32002 
13.33736 
3.098065 
0.036289 
4.289567 
78.35048 
Advertising 
0.013242 
0.327592 
0.040422 
0.969694 
0.8963 
0.922782 
The estimated regression equation is given below;
 Determine whether the model is significant overall. Use α = 0.10. (2 marks)
Answer
ANOVA 






df 
SS 
MS 
F 
Significance F 
Regression 
2 
45.35284 
22.67642 
6.716801 
0.052644 
Residual 
4 
13.5043 
3.376075 


Total 
6 
58.85714 



As can be seen I the above table, the pvalue for the Fstatistics is 0.0526 (a value less than α = 0.10), this leads to rejection of the null hypothesis and thus we conclude that the overall model is significant at α = 0.10.
 Determine if competitor’s price and advertising is individually significantly related to sales. Use α = 0.10. (2 marks)
Answer

Coefficients 
Standard Error 
t Stat 
Pvalue 
Lower 95% 
Upper 95% 
Intercept 
3.597615 
4.052244 
0.887808 
0.424805 
7.65322 
14.84845 
Price 
41.32002 
13.33736 
3.098065 
0.036289 
4.289567 
78.35048 
Advertising 
0.013242 
0.327592 
0.040422 
0.969694 
0.8963 
0.922782 
The pvalue for the price is 0.036 (a value less than α = 0.10), this leads to rejection of the null hypothesis and thus we conclude that competitor’s price is individually significantly related to sales at α = 0.10.
The pvalue for the advertising is 0.9697 (a value greater than α = 0.10), this leads to nonrejection of the null hypothesis and thus we conclude that advertising is individually not significantly related to sales at α = 0.10.
 Based on your answer to part (c), drop any insignificant independent variable(s) and reestimate the model. What is the new estimated regression equation? (2 marks)
Answer
We drop the advertising and the new results as shown below;
SUMMARY OUTPUT 



Regression Statistics 

Multiple R 
0.877761 
R Square 
0.770464 
Adjusted R Square 
0.724557 
Standard Error 
1.643765 
Observations 
7 
ANOVA 






df 
SS 
MS 
F 
Significance F 
Regression 
1 
45.34733 
45.34733 
16.78311 
0.009385 
Residual 
5 
13.50981 
2.701963 


Total 
6 
58.85714 




Coefficients 
Standard Error 
t Stat 
Pvalue 
Lower 95% 
Intercept 
3.581788 
3.608215 
0.992676 
0.366447 
5.69342 
Price 
41.60305 
10.15521 
4.096719 
0.009385 
15.49825 
The estimated regression equation is given below
 Interpret the slope coefficient(s) of the model from part (d). (1 marks)
Answer
The slope coefficient for the competitor’s price is 41.6031; this implies that a unit increase in the competitor’s price would result to an increase in the sales made by 41.6031. Similarly, a unit decrease in the competitor’s price would result to a decrease in the sales made by 41.6031.
Follow Us