Comprehensive Data Analysis: Distribution, Regression, Hypothesis Test

This assignment solution covers various aspects of data analysis, including frequency distribution tables with relative and percent frequency, histogram interpretation, and the selection of appropriate measures like the median for skewed distributions. It also addresses hypothesis testing using F-tables to determine the relationship between demand and price, calculating the coefficient of determination to quantify the variation in the dependent variable explained by the independent variable, and computing the correlation coefficient. Furthermore, the solution includes an ANOVA test to compare means across different treatments and a regression analysis to model the number of phones sold based on price and advertising spots, including tests for model and coefficient significance and interpreting the gradient of coefficients. Desklib offers a wealth of similar solved assignments and study resources for students.

Data analysis 1
Name
Tutor
Institution
Date

Data analysis 2
NUMBER 1
a. Frequency distribution table showing relative frequency and percent frequency
distribution
Class Frequency Relative frequency % frequency
123 - 173 9 0.18 18%
174 - 224 15 0.3 30%
225 - 275 11 0.22 22%
276 -326 5 0.1 10%
327 - 377 4 0.08 8%
378 - 428 2 0.04 4%
429 - 479 3 0.06 6%
480 - 530 1 0.02 2%
Table 1
b. Percent frequency distribution for furniture order values histogram
123 -
173 174 -
224 225 -
275 276 -
326 327 -
377 378 -
428 429 -
479 480 -
530
0%
5%
10%
15%
20%
25%
30%
35%
Histogram
Class
Percentage frequency
Figure 1
It can be observed that the distribution curve above is not normal. The curve is skewed
to the right. This indicates that the order values are not normally distributed.
c. Since the shape is skewed to the right it means that there are extreme values on
the right. Extreme values always affect the mean hence rendering it unfit for

Data analysis 3
measure. The median is the best measure for this distribution because it is
resistant to outliers.
QUESTION 2
a. Since F (2, 47) = 74.13, from F-tables, the p-value is 0.000. This value is less
than alpha value (0.05). We are therefore guided not to accept the null
hypothesis. Conclusion: demand and price are related.
b. Finding the Coefficient of determination
Coefficient of determination= RSS
Rtotal
=5048.818
8181.479 =0.617
The value 0.617 indicates that demand which is the independent variable is responsible
for 61.7% of variation that occurs in price which is the dependent variable.
c. The coefficient of correlation
coefficient of cor relation= standard error
coefficient of determination
¿ 0.248
0.617 =0.4
QUESTION 3
Hypothesis
H0: Mean1 = Mean2 = Mean3
Versus
H1: At least one treatment has a different mean
Since F (2, 23) = 16.43, from F-tables, the p-value is 0.000. This value is less than
alpha value (0.05). We are therefore guided not to accept the null hypothesis.
Conclusion: at least one mean is different.

Data analysis 4
QUESTION 4
a. The regression equation
Number of phones sold=0.4977 ( price ) +0.4733 ( no . of advertising spots )+ 0.8051
b. Test for significance of the model
Because F (2,102) = 63.06, p < 0.001. Conclusion: the model is significant at 0.05 level
of significance
c. Test significance of coefficients
Because 0.001< 0.05, it can be concluded that 1 and 2 are significantly different from
zero.
d. Gradient of coefficient of X2
The gradient is 0.4733. This indicates that a single unit change in the number of
advertising spots causes a corresponding 0.4733 unit change in the number of
phones sold.
e. Number of phones sold
number of phones sold=0.4977 ( 20,000 ) +0.4733 ( 10 ) +0.8051
number of phones sold=9,959.54∨9960