Determining the distribution of furniture orders
1. a) Frequency table
| Classes | Frequency | Relative Frequency | Percentage Relative Frequency |
| 100 to 150 | 3 | 0.06 | 6 |
| 150 to 200 | 15 | 0.3 | 30 |
| 200 to 250 | 14 | 0.28 | 28 |
| 250 to 300 | 6 | 0.12 | 12 |
| 300 to 350 | 4 | 0.08 | 8 |
| 350 to 400 | 3 | 0.06 | 6 |
| 400 to 450 | 3 | 0.06 | 6 |
| 450 to 500 | 2 | 0.04 | 4 |
| Total | 50 | 1 | 100 |
c) Histogram
The asymmetric shape of the histogram indicated above is established from the length of the right tail exceeding that of the left tail. This corresponds to presence of positive skew and potential presence of positive side outliers (Taylor and Cihon, 2014).
c) The suitable central tendency measure needs to be outlined. The choice is between mean and median. Here, median would be the appropriate choice considering that the underlying data is skewed and hence the mean would be vulnerable to extremely high values which is not an issue with median (Lehman and Romano, 2016).
2. Regression Model
|
ANOVA |
||||
|
df |
SS |
|||
|
Regression |
1 |
5048.818 |
||
|
Residual |
46 |
3132.661 |
||
|
Total |
47 |
8181.479 |
||
|
Coefficients |
Standard Error |
t value |
p value |
|
|
Intercept |
80.39 |
3.102 |
25.916 |
0.000 |
|
X |
-2.137 |
0.248 |
-8.617 |
0.000 |
| ANOVA | ||||
| df | SS | |||
| Regression | 1 | 5048.818 | ||
| Residual | 46 | 3132.661 | ||
| Total | =SUM(B3:B4) | =SUM(C3:C4) | ||
| Coefficients | Standard Error | t value | p value | |
| Intercept | 80.39 | 3.102 | =B8/C8 | =T.DIST(D8,B5,FALSE ) |
| X | -2.137 | 0.248 | =B9/C9 | =T.DIST(D9,B5,FALSE) |
The relevant hypotheses for performing hypothesis test are listed below.
The slope coefficient corresponding to unit price has a test statistics value of -8.617 which yields the p value as 0.000. Thus, the evidence indicates rejection of H0 thus paving way for acceptance of H1 (Koch, 2013).
Conclusion:
The linear relationship between the two variables is significant in statistical terms owing to slope being non-zero.
b) For the regression model, the coefficient of determination is determined as highlighted below:
The given regression model has the capability to account to explain 61.7% changes in the unit demand using price as the suitable predictor variable (Harmon, 2011).
c) For the regression model, the coefficient of correlation is determined as highlighted below:
Considering the above computations, the appropriate value of correlation coefficient is -0.786 and this value has been selected considering that regression line is downward sloping as evident from the slope (Lind, Marchal and Wathen, 2012).
| Source of variation | Sum of squares | Degree of Freedom | Mean Square | F | Significance F |
| Between Treatments | 390.58 | 2 | 195.29 | 25.89 | 0.00 |
| Within Treatment (Error) | 158.40 | 21 | 7.54 | ||
| Total | 548.98 | 23 |
| Source of variation | Sum of squares | Degree of Freedom | Mean Square | F | Significance F |
| Between Treatments | 390.58 | 3-1 | =B2/C2 | =D2/D3 | =F.DIST(E2,C2,C3,FALSE) |
| Within Treatment (Error) | 158.4 | 24-3 | =B3/B3 | ||
| Total | =SUM(B2:B3) | 23 |
Test statistics (For ANOVA based on the above output) = 25.89
Corresponding p value (For ANOVA based on the above output) = 0.00
Conclusion:
It would not be appropriate that the means across the different populations is same as the statistical evidence suggests that one least one population mean shows a significant deviation (Koch, 2013).
| n | 7 | ||||
| k | 2 | ||||
| ANOVA | |||||
| df | SS | MS | F | Significance F | |
| Regression | 2 | 40.7000 | 20.3500 | 80.1181 | 0.0000 |
| Residual | 4 | 1.0160 | 0.2540 | ||
| Coefficients | Standard Error | t value | p value | ||
| Intercept | 0.8051 | ||||
| X1 | 0.4977 | 0.4617 | 1.0780 | 0.2060 | |
| X2 | 0.4733 | 0.0387 | 12.2300 | 0.0000 |
a) Regression equation based on intercept and slope coefficients is given below:
b) Total data has taken for one week i.e. for n = 7 days and hence,
The degree of freedom (Regression) = k = 2
The degree of freedom (Residual) = 7-2-1 =4
The relevant hypotheses for performing hypothesis test are listed below.
Test statistics (For ANOVA based on the above output) = 80.118
Corresponding p value (For ANOVA based on the above output) = 0.00
Conclusion:
The multiple regression model highlighted above is significant owing to existence of atleast one non-zero slope coefficient.
The slope coefficient corresponding to unit price has a test statistics value of 1.078 which yields the p value as 0.206. Thus, the evidence indicates non-rejection of H0.
Conclusion:
The linear relationship between the two variables is insignificant in statistical terms owing to slope being assumed as zero.
The slope coefficient corresponding to unit price has a test statistics value of 12.23 which yields the p value as 0.000. Thus, the evidence indicates rejection of H0 thus paving way for acceptance of H1.
Conclusion:
The linear relationship between the two variables is significant in statistical terms owing to slope being non-zero.
d) Slope coefficient for advertising spots :
Interpretation: The above coefficient highlights that daily sales of mobile can witness an increase/decrease of 0.4733 units provided the advertising spots undergo an increase/decrease of 1 unit (Harmon, 2011).
e) Regression equation
References
Harmon, M. (2011) Hypothesis Testing in Excel – The Excel Statistical Master 7th ed. Florida: Mark Harmon.
Koch, K.R. (2013) Parameter Estimation and Hypothesis Testing in Linear Models 2nd ed. London: Springer Science & Business Media.
Lehman, L. E. and Romano, P. J. (2016) Testing Statistical Hypotheses 3rd ed. Berlin : Springer Science & Business Media.
Lind, A.D., Marchal, G.W. and Wathen, A.S. (2012) Statistical Techniques in Business and Economics 15th ed. New York: McGraw-Hill/Irwin.
Taylor, K. J. and Cihon, C. (2014) Statistical Techniques for Data Analysis 2nd ed. Melbourne: CRC Press.
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