Statistics Report: Descriptive Analysis and Hypothesis Testing

This report presents a comprehensive statistical analysis of car data, focusing on descriptive analysis, hypothesis testing, and model building. The report begins with an introduction to statistics and the variables used in the analysis: price, horsepower, curb weight, and speed. Descriptive analysis is performed on price and speed. The report then explores three types of hypothesis tests: Chi-square, t-test, and ANOVA, although the specific results for each test are not fully detailed. Finally, the report presents three regression models to predict the price of cars based on curb weight, horsepower, and speed. The report provides regression statistics, ANOVA tables, and residual outputs for each model, offering insights into the relationships between the variables and the models' predictive capabilities. The conclusion summarizes the key findings regarding the systematic process of gathering, collecting, analysing and developing results for different dependent and independent variables.

Statistics

Contents
INTRODUCTION...........................................................................................................................1
TASK...............................................................................................................................................1
Question 1...............................................................................................................................1
Question 2...............................................................................................................................1
Question 3...............................................................................................................................2
Question 4.............................................................................................................................10
Conclusion.....................................................................................................................................14

INTRODUCTION
In data analysis, a division of mathematics that is related with gathering classifying,
analysing and interpreting of numerical figures in order to make meaningful conclusions as per
the probability is known as statistic. The basic statistics includes descriptive analysis, correlation,
hypothesis test for dependent and independent variable which help in extracting suitable results
from large group of numeric information. In this report, descriptive analysis on any 2 interval 3
different hypothesis tests and model to predict an interval are discussed.
TASK
Question 1
In given assessment data of Sport and GT cars is given along with different variables like
price, horsepower, curb weight, speed, manufacture, V8 and GM Product. Here in assessment
major variables Price, Horsepower, Curb weight and Speed. All significant calculations and test
in assessment are conducted by using selected variables. Following are explanation and
relevance of these variables, as discussed below:
Price: This refers to market price or value of different car models.
Horsepower: It relates to power a car's engine produces.
Curb weight: Curb weight is aggregate weight of car with all standard equipments along
with essential operating consumables like transmission oil, motor oil, air
conditioning refrigerant, coolant and often full-tank fuel, while unloaded.
Speed: Car's speed at 1/4 mile (mph).
Question 2
Descriptive analysis
The first and most important part for conducting statistical analyses is descriptive
analysis that gives a detail idea about the distribution of data which support in detecting mistakes
and outliers and ensure to determine the connection among different variables. From the data
available the two variable that are selected for descriptive analysis are Price and Speed at ¼ mile
(mph).
1

Question 3
Different type of Hypothesis test
2

1. Chi-square test
Price and Horsepower
a. 208 cells (100.0%) have expected count less than 5. The minimum
expected count is .06.
Price and Curb weight
a. 256 cells (100.0%) have expected count less than 5. The minimum
expected count is .06.
Price and Speed
3

a. 224 cells (100.0%) have expected count less than 5. The minimum
expected count is .06.
2. t-test
Price and Curb weight
Price and speed
4

Price and Horsepower
3. Analysis of Variance (ANOVA)
5

6

7

8

9

Question 4
Model to predict an interval
Weight Model 1
Coefficients
Standard
Error t Stat
P-
value Lower 95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept 0 #N/A #N/A #N/A #N/A #N/A #N/A #N/A
Curb
Weight
(lb.) 0.013156926 0.001469 8.95673396
2.09E-
07 0.010025949 0.0162879 0.010026 0.016288
RESIDUAL OUTPUT
Observation
Predicted
Price
($1000s) Residuals
Standard
Residuals
1 33.9053973 -8.8704 -0.4900636
2 40.33913393 53.41887 2.95123645
3 37.41829644 3.481704 0.19235396
4 45.24666718 -20.3817 -1.1260276
5 42.70738054 7.436619 0.41085152
6 43.66783611 26.07416 1.44052146
7 42.45739895 -19.2574 -1.0639151
8 40.02336771 -13.6414 -0.7536458
9 42.62843899 2.359561 0.13035886
10 39.79969998 2.9623 0.16365843
11 49.16743102 -1.64943 -0.0911262
12 37.6551211 -12.5891 -0.6955122
10
Regression Statistics
Multiple R 0.917864462
R Square 0.84247517
Adjusted R Square 0.775808503
Standard Error 18.69411976
Observations 16
ANOVA
df SS MS F Significance F
Regression 1 28035.57 28035.57002 80.22308 3.59105E-07
Residual 15 5242.052 349.4701135
Total 16 33277.62

13 45.45717799 -17.6872 -0.977165
14 37.12884408 8.431156 0.46579676
15 46.11502427 -5.12602 -0.2831979
16 43.22050064 -2.1005 -0.1160465
PROBABILITY OUTPUT
Percentile
Price
($1000s)
3.125 23.2
9.375 24.865
15.625 25.035
21.875 25.066
28.125 26.382
34.375 27.77
40.625 40.9
46.875 40.989
53.125 41.12
59.375 42.762
65.625 44.988
71.875 45.56
78.125 47.518
84.375 50.144
90.625 69.742
96.875 93.758
Price model 2
Regression Statistics
Multiple R 0.934476
R Square 0.873246
Adjusted R Square 0.806579
Standard Error 98.98286
Observations 16
ANOVA
df SS MS F
Significance
F
Regression 1 1012478.892 1012479 103.3394 7.62E-08
Residual 15 146964.1081 9797.607
Total 16 1159443
11

Coefficients
Standard
Error t Stat P-value
Lower
95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept 0 #N/A #N/A #N/A #N/A #N/A #N/A #N/A
Price
($1000s) 5.515906 0.5426051 10.1656
4.02E-
08 4.359371 6.672441 4.359371 6.672441
RESIDUAL OUTPUT
Observation
Predicted
Horsepower Residuals
Standard
Residuals
1 138.0907 56.90929581 0.593796
2 517.1603
-
227.1603053 -2.37021
3 225.6006
-
36.60055128 -0.38189
4 137.153 167.8469998 1.75133
5 276.5896 68.41041458 0.7138
6 384.6903 65.30969077 0.681447
7 127.969 97.03098314 1.012429
8 145.5206 49.47937056 0.516272
9 248.1496 -33.1495746 -0.34589
10 235.8712
-
50.87116807 -0.53079
11 262.1048 57.89518348 0.604083
12 138.2617 16.73830273 0.174649
13 153.1767 151.8232932 1.584137
14 251.3047
-
50.30467277 -0.52488
15 226.0915 93.90853309 0.97985
16 226.8141 9.185949419 0.095847
PROBABILITY OUTPUT
Percentile
Horsepowe
r
3.125 155
9.375 185
15.625 189
21.875 195
28.125 195
12

34.375 201
40.625 215
46.875 225
53.125 236
59.375 290
65.625 305
71.875 305
78.125 320
84.375 320
90.625 345
96.875 450
Speed Model 3
Regression Statistics
Multiple R 0.935359
R Square 0.874896
Adjusted R Square 0.808229
Standard Error 16.65967
Observations 16
ANOVA
df SS MS F
Significance
F
Regression 1 29114.45 29114.45 104.9 6.94E-08
Residual 15 4163.171 277.5447
Total 16 33277.62
Coefficients
Standard
Error t Stat P-value
Lower
95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept 0 #N/A #N/A #N/A #N/A #N/A #N/A #N/A
Speed at
1/4 mile
(mph) 0.435504 0.042521 10.24207
3.64E-
08 0.344872 0.526135 0.344872 0.526135
RESIDUAL OUTPUT
Observation
Predicted
Price
($1000s) Residuals
Standard
Residuals
13

1 39.5002 -14.4652 -0.89675
2 47.03442 46.72358 2.89657
3 40.58896 0.31104 0.019283
4 44.944 -20.079 -1.24477
5 44.46494 5.679056 0.352066
6 50.60555 19.13645 1.18634
7 39.9357 -16.7357 -1.03751
8 39.0647 -12.6827 -0.78625
9 40.50186 4.486141 0.278113
10 40.19701 2.564994 0.159014
11 43.11488 4.403118 0.272966
12 36.84363 -11.7776 -0.73014
13 44.944 -17.174 -1.06468
14 40.58896 4.97104 0.308173
15 45.72791 -4.73891 -0.29378
16 42.24387 -1.12387 -0.06967
PROBABILITY OUTPUT
Percentile
Price
($1000s)
3.125 23.2
9.375 24.865
15.625 25.035
21.875 25.066
28.125 26.382
34.375 27.77
40.625 40.9
46.875 40.989
53.125 41.12
59.375 42.762
65.625 44.988
71.875 45.56
78.125 47.518
84.375 50.144
90.625 69.742
96.875 93.758
14

Conclusion
From the above report, it has been concluded that statistical is a systematic process of
gathering, collecting, analysing and developing results for different dependent and independent
variables. Hypothesis testing mainly related to formal process that is used to accept or reject the
statistical hypothesis.
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