Statistics Group Project TASK 13 (a) Survey method3 (b) Sampling method3 (c) Sample selection method3 (c) Estimation errors 13 (a) Coefficient of resoluteness for grade of exem

Statistics Group Project TASK 13 (a) Survey method3 (b) Sampling method for selecting a sample: 3 (c) Determination of the dependentandindependent variablesand identification of the data type: 4 (d) Issues 4 (e) Frequency histogram5 (f) Scatter plot : 7 (g) Equation of estimated fitting line : 8 (h) Summary11 (i) Interpretation: 13 TASK 213 (a) Estimate errors 13 (b) Coefficient 13

Statistics Group Project

Table of Contents
TASK 1............................................................................................................................................3
(a) Survey method..................................................................................................................3
(b) Sampling method for selecting a sample:.........................................................................3
(c) Determination of the dependent and independent variables and identification of the data
type:........................................................................................................................................4
(d) Issues ................................................................................................................................4
(e) Frequency histogram ........................................................................................................5
(f) Scatter plot :.......................................................................................................................7
(g) Equation of estimated fitting line :...................................................................................8
(h) Summary ........................................................................................................................11
(i) Interpretation:..................................................................................................................13
TASK 2..........................................................................................................................................13
(a) Estimate errors................................................................................................................13
(b) Coefficient......................................................................................................................13
(c) Attuned coefficient of resoluteness for grade of exemption:..........................................14
(d) ........................................................................................................................................15
(e) .........................................................................................................................................15
(f) Relation between tallness of father and son....................................................................16
(g) Relation between tallness of Mother and son:................................................................17

TASK 1
(a) Survey method
The survey method may be in two forms such as questionnaire and interviews. There will
be questionnaire method was select to conduct a survey. Questionnaire contains a number of
questions in sequence about various aspects. These questionnaire are presented to the
respondents and collected their reviews through these questions. The questionnaire may be in
form of printed paper or electronic. It may be emailed to various respondents if physically
distribution is not possible. It also provide choice of answers to the respondents so that they can
make easy decision while filling up the questionnaire. Questionnaire may be of various types
such as customer satisfaction questionnaire, product use satisfactory questionnaire, company
communication evaluation questionnaire, etc.. on the other hand it contain some specific
characteristics such as uniformity, exploratory, questions sequencing, etc..
(b) Sampling method for selecting a sample:
There are two types of sampling methods such as probability and non-probability.
Probability based techniques are more useful and reliable. Following are the probability based
techniques:
 Random sampling: As the name indicate that method is very simple which based on
totally selection of sample from individuals through automated process. The sample is
selected on random basis.
 Stratified sampling: This type of sampling method used when there was a large size of
population. According to that sampling technique the whole population are divided into
small strata and then sample is chosen from each group.
 Cluster sampling: that type of method contains the random selection of samples from
geographical spread variables.
Probability based sampling methods are more reliable because these provides the total population
based sample which present the guaranteed results based on whole population.
There are some specific steps to conduct probability sampling, which are as follows:
1. choosing of interested population carefully.
2. Determination of appropriate sample frame.
3. Selection of sample according to sample frame and start up of survey.

(c) Determination of the dependent and independent variables and identification of the data type:
The data are given for the preparation time and marks of students. The values which
does not consider by researcher is known as dependent variable. Independent variable are those
values which can be manipulated in experiment. Both the variables are important for the
interpretation of results, but the data given for the preparation time are independent in nature and
marks of the students are dependent.
Why? - The data for marks of the students are dependent and data for preparation time is
independent because the marks of students depends on the preparation of students. As the more
preparation students done they get more marks and if they give less time to their preparation then
they get less marks. So the data of marks of students is depend on the data of preparation time.
So that the dependent variables are marks of students and independent variables preparation of
data.
Data types : Variable is numerical in context to type of data.
(d) Issues
1. Lack of attention
2. Dishonesty
3. Differences in understanding and interpretation
4. Problems in expressing felling and emotions
5. Difficulty in analysing some questions
6. Biasses
7. Lack of personal relation with respondents
8. Accessibility issues
Explanation of two cases: Following are the explanation of two cases from the list of issues
which faced due to data collection with the help of questionnaire method:
Dishonesty: The foremost problem with this method is that the respondents are not
honest every time. Most of the respondents answers without any truthfulness and proper
attention. So the whole survey goes in wrong direction.
Differences in understanding and interpretation: most of the respondents interpret the
presented questions in wrong way so that answers were fluctuate according to distinct point of
view of respondents and researcher.

(e) Frequency histogram
Marks F RF CF CRF
20-30 4 4% 4 4%
30-40 8 8% 12 12%
40-50 11 11% 23 23%
50-60 15 15% 38 38%
60-70 31 31% 69 69%
70-80 13 13% 82 82%
80-90 10 10% 92 92%
90-100 8 8% 100 100%
Prepartion
time F RF CF CRF
20-30 1 1% 1 1%
30-40 8 8% 9 9%
40-50 16 16% 25 25%
50-60 20 20% 45 45%
60-70 21 21% 66 66%
70-80 18 18% 84 84%
80-90 16 16% 16 16%

90-100 0 0% 0 0%
There are some specific shapes of frequency histogram, which describes also the nature
of distribution.
Comment: In conducted scenario, the shape of frequency histogram is bell shaped which
shows normal distribution.
These shapes are described as follows, which clarify the reason of above comment:

Bell shaped: That type of shape of histogram same as the shape of a bell. It shows the normal
distribution.
Bimodal: That type of shapes shows two different peaks. It shows that the data are from two
different sources, which have to be analysed differently.
Skewed right and left: A distribution skewed to the right is said to be positively skewed. This
type of distribution has huge number of occurrences in lower value cells (left side) & few in the
upper value cells (right side). A skewed distribution can result when data is gathered from a
system with has a boundary such as zero. And on the other hand the left skewed distribution is
totally opposite from it.
Uniform: it shows little information. It occurs when number of classes very small.
Random: This type of distribution is a random distribution, which have no apparent. It have two
many classes.
(f) Scatter plot :
(g) Equation of estimated fitting line :
Descriptive
Statistics
Mean Std.
Deviation
N

PREPARATION
TIME 63.04 16.321 100
MARK 65.74 17.410 100
Correlations
PREPARATI
ON TIME
M
A
R
K
Pearson
Correlation
PREPARATION
TIME 1.000 .547
MARK .547 1.000
Sig. (1-tailed)
PREPARATION
TIME . .000
MARK .000 .
N
PREPARATION
TIME 100 100
MARK 100 100
Model
Summa
ryb
Model R R
Square
Adjuste
d R
Square
Std.
Error of
the
Estimate
Change
Statistic
s
R
Square
Change
F
Change
df1 df2 Sig. F
Change
1 .547a .299 .292 13.737 .299 41.745 1 98 .000
a.
Predicto
rs:
(Consta
nt),
MARK

b.
Depend
ent
Variable
:
PREPA
RATIO
N TIME
ANOVAa
Model Sum of
Squares
df Mean
Square
F S
i
g
.
1
Regression 7877.302 1 7877.302 41.745 .000b
Residual 18492.538 98 188.699
Total 26369.840 99
a.
Dependen
t
Variable:
PREPAR
ATION
TIME
b.
Predictors
:
(Constant)
, MARK
Coefficie
ntsa
Model Unstandardized
Coefficients
Standardized
Coefficients
t S
i
g
.
B Std. Error Beta

1 (Constant) 29.359 5.391 5.446 .000
MARK .512 .079 .547 6.461 .000
a.
Dependen
t Variable:
PREPAR
ATION
TIME
Residuals
Statisticsa
Minimu
m
Maximu
m
Mean Std.
Deviation
N
Predicted Value 42.17 80.59 63.04 8.920 100
Residual -34.346 45.271 .000 13.667 100
Std. Predicted
Value -2.340 1.968 .000 1.000 100
Std. Residual -2.500 3.296 .000 .995 100
a.
Dependent
Variable:
PREPARA
TION
TIME

(h) Summary
Statistics
PREPARATI
ON TIME
M
A
R
K
N Valid 100 100
Missing 0 0
Mean 63.04
6
5
.
7
4
Median 64.00
6
8
.
0
0

Mode 64 7
0
Std. Deviation 16.321
1
7
.
4
1
0
Variance 266.362
3
0
3
.
1
2
4
Range 65 7
5
Minimum 25 2
5
Maximum 90
1
0
0
Sum 6304
6
5
7
4
Percentiles
10 43.00 40.00
20 46.00 50.00
25 49.00 54.00
30 54.00 58.00
40 57.40 62.80
50 64.00 68.00
60 67.00 70.00
70 73.00 73.00
75 76.75 78.00
80 79.00 80.00
90 86.90 89.60

(i) Interpretation:
There are the some important points of correlation coefficient liner as a numeric measure
of the strength of a linear relationship. If the unit of the measurement of one variable change then
correlation coefficient not change. The correlation measures only the strengths of liner
relationship between two variables. Such as the preparation, time and marks of students have a
strong linear relationship. As the correlation is equals to 1 between the marks of students and
preparation time so that there was a strong linear relationship. The direction of the linear
relationship is positive between both the respective variable.
TASK 2
(a) Estimate errors
Standard error of estimation states estimated standard deviation of error term “u” & it can
known as standard error of the regression. Standard Error of Estimate represents variation of
observations and practised to analyse the correctness of estimation made. The accuracy of
estimated figure are associated with standard errors of estimate exhibits.
Formula used to calculate standard error of estimate is:
SQRT (SSE/(n-k))
Steps related to Standard Error
SSE 25843.41
k 2
n 400
N-k 398
SSE/(n-k) 64.9331909548
SQRT(SSE/(n-k)) 8.058113362
In regression equation standard errors has to be minimum reason being errors are
small, meaningful data which reflects mean must identify as standard & on the far side the
data would characteristic of illustrious correspondence.
(b) Coefficient
The coefficient of determination is a tool used in statistical analysis that ensures and
assesses how well a model explains and assists in estimation of future results or outputs. It
represents exact level of related variability in data set. Coefficient of determination known as R-

squared and used to determine accuracy of the model. Coefficient of determination defines
variables in given model as certain percentage of observed variation. Output under coefficient of
determination is represented as a value between 0 and 1 and Closer the value is to 1, the better
the fit, or relationship, between the two factors. Therefore in case the R Square is equal to
0.2672, then approximately less than half of the observed variation can be explained by the
model.
Formula which is required to calculate Coefficient of determination is:
MSS/TSS = (TSS − RSS)/TSS
Following are the steps involved in calculation of Coefficient of determination:
The above table may reflect the MSS model in which different variables are calculated
such as TSS, RSS. Coefficient of determination is the relation between difference between TSS
and RSS and total of TSS. It shows r2=0.27 means 27% of the variability in height of son's can
be explained by differences in father’s height (x1) and mother’s height (x2).
(c) Attuned coefficient of resoluteness for grade of exemption:
Attuned coefficient of resoluteness for grade of exemption is an effective model for
several variables, such as multiple regression model. It shows the percentage of fluctuation in the
dependent or independent variables that are actually affecting each other.
The following table may reflect the calculation of this model:
Adjusted coefficient of determination =
1-(1-0.2672)[(400-1)/400-(2+1)]

0.2635083123
As per given information R-squared and adjusted R-squared are favourable. The Adjusted
R2 can take on negative values, but should always be less than or equal to the Coefficient of
Determination and in given data Adjusted R2 is less than Coefficient of Determination as
calculated in (b) which shows efficiency of data in model.
(d)
As per above table outputs, value of test statistic for testing the overall utility of model, F
= 72.37, the output also includes the P- value of the test, Which is 0.00
As p-value = 0.00 < 0.05 = alpha, hence this model is useful at 5% level of significance.

(e)
Regression coefficients depicts the wave in mean in outcome unsettled for one unit of
change in forecaster covariant while retaining other prognosticator in the exemplary constant.
This is very important because it distinguish between the role of one variable and all of the
others variables in fixation model. A coefficient that shows positive response represents that
increment in the value of the autarkical variable, mean of the mutualist variable also leads to the
raise in the value. A coefficient that shows a negative result indicates that decrement in
dependent variable leads to the increment in independent variable. Coefficient value suggest the
extent to which the mean of the dependent variable changes given a one-unit shift in the
independent variable while holding other variables in the model constant. Coefficients helps to
determine the relation between two variables that are dependent or independent whether it is
positive or negative. A short interpretation of coefficients is as follows:
The above table may reflects overall goodness-of-fit measures:
R2 = 0.2672
When squared R is given 0.2672 then correlation or multiple R will be 0.5169,
Attuned R2 = R2 - (1-R2 )*(k-1)/(n-k) = 0.2635
The modular mistake here denotes that forecasted standard deviation of the error term u.
Sometimes it cal also be called an standard error of the arrested development. There is no need to
get confused with this error of y or other errors of regression that are provided below:
R2 = 0.2672 means that 26.72% of the variation of Y is explained by the regress-ors X1 and X2.
(f) Relation between tallness of father and son
Regression line to show relation between tallness of father and son is:

y = b0 + b1x
y = 93.8993 + 0.4849x
When there is no linear relations between these two variables, then b1 will be equals to 0.
When a relation between these variable is figured out then b1 will not be equals to 0. So this
information allow the data point professional persons to derive that the tallness of father and son
are geometrically connected.
(g) Relation between tallness of Mother and son:
The Abnormality line for showing relationship between Relation between tallness of
Mother and son is:
y = b0 + b1X
y = 93.8993 + (-0.0229) x
When there is no additive relation between these two variables then b1 will be equals
to 0. If there is a additive relation between these two variables then bi will not be equals to
0. So this information allows the data point professionals to generalize that tallness of
mother and son are geometrically connected but there is a antagonistic correlation.