Data Analysis: Frequency Tables, Regression Analysis, Hypothesis Testing

This article covers data analysis techniques such as frequency tables, regression analysis, and hypothesis testing. It includes examples and explanations of each technique.

Data analysis 1
Name
Tutor
Institution
Date

Data analysis 2
NUMBER ONE
a. Frequency table
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. Histogram for percentage frequency
123 -
173 174 -
224 225 -
275 276 -
326 327 -
377 378 -
428 429 -
479 480 -
530
0%
5%
10%
15%
20%
25%
30%
35%
% frequency
Class
Frequency
Figure 1
The frequency histogram above shows the distribution of order values for furniture. As
can be observed the distribution has a long tail to the right hence skewed distribution.
c. The appropriate measure for central tendency is the median. This is because the
distribution is not normal.

Data analysis 3
NUMBER TWO
a. The calculated statistics is F (2, 47) = 74.13. The p-value is 0.000. Since the p-
value is less than the level of significance (0.05), the null hypothesis is not
accepted. The conclusion is therefore that demand and price are related.
b. Finding R-square or the Coefficient of determination
R−square= RegressionSS
Regressiontotal
=5048.818
8181.479 =0.617
R-square value of 0.617 means that 61.7% of change in demand is caused by price.
Price is the independent variable while demand is the dependent variable.
The coefficient of correlation
coefficient of correlation= standard error
coefficient of determination
¿ 0.248
0.617 =0.4
NUMBER THREE
Hypothesis
H0: μ1 = μ2 = μ3
Versus
H1: At least one treatment has a different mean
The calculated statistics is F (2, 23) = 16.43. The p-value is 0.000. Since the p-value is
less than the level of significance (0.05), the null hypothesis is not accepted. It is
concluded that at least one mean is different. The conclusion is therefore that demand
and price are related.

Data analysis 4
NUMBER FOUR
a. Simple linear regression model
y=0.4977 ( X1 ) +0.4733 ( X2 ) + 0.8051
y=number of phones sold
X1 =price
X2 =Number of advertising spots
b. Significance of the model
The calculated statistics is F (2, 102) = 63.06. The p-value is 0.001. Since the p-value
is less than the level of significance (0.05), we conclude that the model is significant.
c. Test significance of coefficients
Comparing p-value 0.001 with alpha value (0.05), it is found that 0.001 < 0.05. It is
concluded that 1 and 2 are significant.
d. The coefficient of X2 (number of advertising spots)
The coefficient of 0.4733 means that a unit change in number of advertising
spots causes a 0.4733 unit change in dependent variable (phone sales).
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