Below you are given the examination scores of 20 students
52 |
99 |
92 |
86 |
84 |
63 |
72 |
76 |
95 |
88 |
92 |
58 |
65 |
79 |
80 |
90 |
75 |
74 |
56 |
99 |
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).
ANOVA |
|
|
|
df |
SS |
Regression |
1 |
354.689 |
Residual |
39 |
7035.262 |
|
Coefficients |
Standard Error |
Intercept |
54.076 |
2.358 |
X |
0.029 |
0.021 |
a. |
What has been the sample size for this problem? |
b. |
Determine whether or not supply 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. |
e. |
Predict the supply (in units) when the unit price is $50,000. |
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
Program A |
Program B |
Program C |
Program D |
150 |
150 |
185 |
175 |
130 |
120 |
220 |
150 |
120 |
135 |
190 |
120 |
180 |
160 |
180 |
130 |
145 |
110 |
175 |
175 |
a. |
Construct an ANOVA table. |
b. |
As the statistical consultant to Allied, what would you advise them? Use a .05 level of significance. |
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
|
Week |
Price |
Advertising |
Sales |
|
1 |
.33 |
5 |
20 |
|
2 |
.25 |
2 |
14 |
|
3 |
.44 |
7 |
22 |
|
4 |
.40 |
9 |
21 |
|
5 |
.35 |
4 |
16 |
|
6 |
.39 |
8 |
19 |
|
7 |
.29 |
9 |
15 |
a. |
What is the estimated regression equation? Show the regression output. |
|||
b. |
Determine whether the model is significant overall. Use α = 0.10. |
|||
c. |
Determine if competitor’s price and advertising is individually significantly related to sales. Use α = 0.10. |
|||
d.
e. |
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). |
The histogram above clearly refers to the presence of positive skew due to which the shape of the graph is asymmetric. This can be inferred from a right side tail which is present. Hence, it ca also be concluded that the above distribution cannot be termed as normal distribution.
(b) The value of coefficient of determination
Correlation of determination
The sign of coefficient of correlation would depend on the sign of independent variable slope coefficient. Therefore, the negative sign of slope coefficient (unit price) implies that the coefficient of correlation is negative (). price. This refers to the lower price beig conducive to higher demand.
(d) The x2 slope coefficient is indicative of the fact that the change in the mobile phone advertising spots tends to bring about a change in the daily sales of mobile phone by 0.4733 units. The direction of change for these two variables is the same owing to positive value of the slope coefficient.
(e) Number of mobile set sold for mobile unit price of $20,000 and 10 advertising spots.
Therefore, 9960 is the total number of mobile sets sold for mobile unit price of $20,000 and 10 advertising spots.
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