Statistical Data Analysis Assignment: Regression and ANOVA Analysis

This document presents a comprehensive solution to a data analysis assignment, covering various statistical techniques. The solution begins with an analysis of frequency distribution, including class width, frequency, and cumulative frequency, followed by a frequency histogram. It then proceeds to address regression analysis, including t-tests, ANOVA, and the interpretation of coefficients and correlation. The assignment also includes calculations and interpretations of R-squared values and the coefficient of correlation. Furthermore, the solution delves into ANOVA (Analysis of Variance) to determine significant differences between groups, as well as multiple regression analysis, interpreting coefficients, p-values, and model significance, and how price and advertising affect sales. The document provides detailed steps, formulas, and interpretations for each statistical method, making it a valuable resource for students studying statistics and data analysis. It also references a source for further information on normal distribution.

Running head: DATA ANALYSIS 1
Data Analysis
Name
Institution

DATA ANALYSIS 2
Data Analysis
Q1 (a)
Class
width
Frequenc
y
Cumulative
Frequency
relative frequency
distribution % frequency distribution
50-59 3 3 0.15 15.00%
60-69 2 5 0.25 25.00%
70-79 6 11 0.55 55.00%
80-89 4 15 0.75 75.00%
90-99 5 20 1 100.00%
Q1 (b)
50-
59 60-
69 70-
79 80-
89 90-
99
0
2
4
6
8
0.00%
40.00%
80.00%
120.00%
Histogram
Frequency
Cumulative %
Bin
Frequency
The shape of the above histogram follows the shape of a normal distribution curve, that is, it is
bell-shaped, symmetric, unimodal, and asymptotic. (Mahajan, 2010).

DATA ANALYSIS 3
Q2 (a)
Sample size for this problem is 40 respondents
Q2 (b)
We conduct t-test
ANOVA
df SS
Regression 1 354.689
Residual 39 7035.262
Coefficients Standard Error
Intercept 54.076 2.358
X 0.029 0.021
Y=a+bx
Ho:B= 0
Ha:B≠0
t= (0.029/0.021)= 1.380952381 which is > α 0.05
Thus, we conclude that demand and unit price are related.
Q2 (c)
Residual Sum of Square(RSS)
354.68
9
Sum of Squared Errors (SSE)
7035.2
6
Total Sum of Squares (TSS)
7389.9
51
R2= (TSS-SSE)/TSS
R2= (7389.951-7035.26)/ 7389.951
R2= 0.047996123
Interpretation; 4.7 % of variation in demand is explained by variation in price
Q2 (d)

DATA ANALYSIS 4
Coefficient of correlation (r) = square root of r2
Hence r= √047996123 =0.219080176
Interpretation; there is a weak relationship between price and demand since the coefficient of
correlation is not close to +1.
Q2 (d)
Supply (in units) when the unit price is $50,000;
Y=mx+c
Y=0.029(50,000) + (54.076)*1000
=1,504,076 units
Q3 (a)
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 P-value F crit
Between Groups 8750 3 2916.667 6.140351 0.00557 3.238872
Within Groups 7600 16 475
Total 16350 19
Q3 (b)
F-calculated 6.14 is greater that F-critical hence there is a significant difference between the 4
groups.
Q4 (a)
Coefficien
ts
Standar
d Error t Stat P-value
Lower
95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept 3.597615
4.05224
4
0.88780
8
0.42480
5
-
7.65322
14.8484
5
-
7.65322
14.8484
5
Price 41.32002
13.3373
6
3.09806
5
0.03628
9
4.28956
7
78.3504
8
4.28956
7
78.3504
8

DATA ANALYSIS 5
Advertising 0.013242
0.32759
2
0.04042
2
0.96969
4 -0.8963
0.92278
2 -0.8963
0.92278
2
The equation of the line becomes y=3.598+41.32B1+0.013B2
Q4 (b)
ANOVA
df SS MS F
Significan
ce F
Regressi
on 2
45.352
84
22.676
42
6.7168
01 0.052644
Residual 4
13.504
3
3.3760
75
Total 6
58.857
14
Since F-calculated 6.716801 > F-critical 0.052644, we conclude that the model is significant.
Q4 (c)
Coefficie
nts
Standa
rd
Error t Stat
P-
value
Intercept 3.597615
4.0522
44
0.8878
08
0.4248
05
Price 41.32002
13.337
36
3.0980
65
0.0362
89
Advertisi
ng 0.013242
0.3275
92
0.0404
22
0.9696
94
Using α = 0.10, competitor’s price is significant as its p values 0.036 < α = 0.10 i.e. However,
advertising is not significant as its p-value 0.969694> α = 0.10.
Q4 (d)
Coefficien
ts
Standar
d Error t Stat P-value
Intercept 3.581788
3.60821
5
0.99267
6
0.36644
7
Price 41.60305
10.1552
1
4.09671
9
0.00938
5
Based on the new model, the new estimated regression equation becomes

DATA ANALYSIS 6
y=3.598+41.32B1
Q4 (e)
Holding all other factors constant, a unit rise in price of competitor's product (x1) results in 41.32
unit increase of the weekly sales for its product (y).
References
Mahajan, B. (2010). Chapter-05 Normal Distribution and Normal Curve. Methods in
Biostatistics, 8(2), 70-79. doi:10.5005/jp/books/11703_5