shajib final 2

8/3/2019 Shajib Final 2

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1) a)

One-Sample Statistics

N Mean Std.Deviation

Std. Error Mean

Selling Price

in TK. 000(Thousand)

50 2421.616 498.323 70.473

One-Sample Test

Test Value= 0

t df Sig. (2-tailed)

MeanDifference

99%ConfidenceInterval of

theDifference

Lower Upper

SellingPrice in TK.

000(Thousand)

34.362 49 .000 2421.616 2232.751 2610.481

Interpretation: The upper value is 2610.481and the lower value is 2232.751

2232.751 2610.481

If 100 samples of the same size could be taken and similar confidence intervals

were constructed, 99 samples would contain population parameter, mean, which will lie

in the confidence interval of (2232.751-2610.481)

b)



Std. ErrorMean

Size ofthe Homein Square

Feet

50 2220.00 277.01 39.18

One-Sample Test

TestValue = 0


MeanDifference

95%Confidence

Interval ofthe

1


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Difference

Lower Upper

Size of the

Home in

Square Feet

56.669 49 .000 2220.00 2141.27 2298.73

Interpretation: The upper value is 2298.73and the lower value is 2141.27

2141.27 2298.73

If 100 samples of the same size could be taken and similar confidence intervals

were constructed, 95 samples would contain population parameter, mean, which will lie

in the confidence interval of (2141.27-2298.73

2) a)

Step 1

H0: 2200

H1: > 2200 [So, this is a one-tail test]

Step 2

= 0.01

Step 3t statistics is to be used.

Step 4:

Decision Rule: If p value < value (0.01), we reject H0: otherwise it is accepted.



Std. ErrorMean

SellingPrice inTK. 000

(Thousand)

50 2421.616 498.323 70.473

One-Sample Test

Test Value= 2200


MeanDifference

99%Confidence Interval

2


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of theDifference

Lower Upper

SellingPrice inTK. 000

(Thousand)

3.145 49 .003 221.616 32.751 410.481

As it is a 1- tailed test, P- value = .012/2 = 0.006

Decision: Since p value < value, we reject H0. That means the mean selling price in

Gulshan area is more than 2200

b)

Step 1

H0: 2100

H1: > 2100

So, this is a one-tail test

Step 2

= 0.05

Step 3

t statistics is to be used.

Step 4:Decision Rule: If p value < value (0.05), we reject H0 otherwise it is accepted.

Step 5:



Std. ErrorMean

Distance 50 13.90 5.17 .73

One-Sample Test

Test Value= 12


MeanDifference


of theDifference

3


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Lower Upper

Distance 2.598 49 .012 1.90 .43 3.37

As it is a 1- tailed test, P-value = .0012/2 = .006

So, p value < value (0.05) . So, we reject Ho and accept H1. This means the mean

distances of home is less than 15

3) a)

Here we consider, 1 = mean selling price of homes with a pool and

2 = mean selling price of homes without a pool

Ho: 1 = 2

Ha: 1 2

So, this is a two tail test

= 0.01

Decision Rule: Reject Ho if P-value< ; do not reject otherwise.

Paired Samples Statistics

Mean N Std.Deviation

Std. ErrorMean

Pair 1 SellingPrice inTK. 000

(Thousand)

2421.616 50 498.323 70.473

Pool .70 50 .46 6.55E-02

Paired Samples Correlations

NCorrelation Sig.


(Thousand) & Pool

50 .325 .021

Paired Samples Test

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PairedDifference

s

t df Sig. (2tailed

Mean Std.Deviation

Std. ErrorMean


of theDifference

Lower Upper


(Thousand) - Pool

2420.916 498.172 70.452 2279.337 2562.495 34.363 49 .00

Here, the P-value is .000

So, P-value (0.000) < (.05), we reject Ho

Interpretation: At the 0.05 significance level, we can conclude that we have somestrong evidence that there is a difference in the mean selling price of homes with a pool,

and homes without a pool.

b)

Here we consider, 1 = mean selling price of homes with an attached garage and2 = mean selling price of homes without a garage

Ho: 1 = 2H1: 1 2

So, this is a two-tail test

= 0.01

Decision Rule: Reject Ho if P- value< ; do not reject otherwise.

Paired Samples Statistics

Mean N Std.Deviation

Std. ErrorMean


(Thousand)

2421.616 50 498.323 70.473

GarageAttached

.72 50 .45 6.41E-02

Paired Samples Correlations

NCorrelation Sig.

5


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(Thousand) & Garage

Attached

50 .531 .000

Paired Samples Test

PairedDifference

s

t df Sig. (2tailed

Mean Std.Deviation

Std. ErrorMean


of theDifference

Lower Upper


(Thousand) - Garage

Attached

2420.896 498.082 70.439 2232.122 2609.670 34.368 49 .000

From the table we find that P-value is 0.000

So, P-value (0.000) < (0.01), we reject Ho

Interpretation: At the 0.01 significance level, we can conclude that we have some strong

evidence that there is a difference in the mean selling price of homes with an attached

garage and homes without a garage.

4) a)

Here we consider, 1 = mean selling price of homes with a pool and

2 = mean selling price of homes without a pool

Ho: 1 = 2

H1: 1 2

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So, this a two-tailed test

= 0.01

Decision Rule: Reject Ho if P-value < ; Otherwise accept H1

ANOVASelling Price in TK. 000 (Thousand)

Sum ofSquares

df MeanSquare

F Sig.

BetweenGroups

1289149.632

1 1289149.632

5.688 .021

WithinGroups

10878792.235

48 226641.505

Total 12167941.867 49

From the table, we found P-value = 0.021

Decision: Since the P-value = 0.021 > , we accept Ho.

Interpretation: At the 0.01 significance level, we can conclude that there is no

difference in the variability of the selling prices of homes that have a pool versus thosethat do not have a pool.

b)

H0: 1 = 2 = 3 = 4 = 4 = 5 [ 1 = Mean price of Gulshan,

2 = Mean price of Uttara,

3 = Mean price of DOHS,

4 = Mean price of Dhanmondi,

5 = Mean price of Banani]

H1: 1 2 3 4 4 5

So it is a two-tailed test.

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= 0.01

Decision Rule: Reject Ho if P-value . So, we accept Ho

Interpretation: At the 0.01 significance level, we can conclude that we have some

strong evidence that there is no difference in the mean selling prices of homes among the

five townships.

5) a)

Variables Entered/Removed

Model VariablesEntered

VariablesRemoved

Method

1 Distance,Number ofBedrooms,Size of the

Home inSquare

Feet

. Enter

a All requested variables entered.

b Dependent Variable: Selling Price in TK. 000 (Thousand)

Coefficients

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Unstandardized

Coefficients

Standardized

Coefficients

t Sig.

Model B Std. Error Beta

1 (Constant) 1447.182 508.646 2.845 .007

Number ofBedrooms 136.413 37.134 .442 3.674 .001

Size of theHome inSquare

Feet

.356 .218 .198 1.631 .110

Distance -26.036 10.862 -.270 -2.397 .021

a Dependent Variable: Selling Price in TK. 000 (Thousand)

Regression equation =

Y= a+1X1+ 2X2+ 3X3+..+ kXk

Here,we have 3independent variables size of home,distance and number of bedrooms.

So regression equation here is

Y= a+1X1+ 2X2+ 3X3

=1447.182+136.413+-.356-26.036

=1557.915

b)

Variables Entered/RemovedModel Variables

EnteredVariablesRemoved

Method

1 Distance,Number ofBedrooms,Size of the

Home inSquare

Feet

. Enter

a All requested variables entered.


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Number ofBedrooms


Feet

Distance Number ofBedrooms

Number ofBedrooms

PearsonCorrelation

1.000 .328 -.198 .310

Sig. (2-tailed) . .014 .144 .020

N 56 56 56 56

Size ofthe Homein Square

Feet

PearsonCorrelation

.328 1.000 -.105 .002

Sig. (2-tailed)

.014 . .443 .988

N 56 56 56 56

Distance PearsonCorrelation

-.198 -.105 1.000 -.374

Sig. (2-

tailed)

.144 .443 . .005

N 56 56 56 56

Number ofBathrooms

PearsonCorrelation

.310 .002 -.374 1.000

Sig. (2-tailed)

.020 .988 .005 .

N 56 56 56 56

Correlation is significant at the 0.05 level (2-tailed).

Correlation is significant at the 0.01 level (2-tailed).

From the above table we get the Correlation of variables:

Correlation of number of bedrooms is 1.000. This indicates perfect positive correlation.Correlation of Size of the Home in Square Feet is .328 which indicates weak positive correlation.Correlation of distance is -.198. Which indicates weak negative correlation.Correlation of Number of Bathroom is .988 which indicates strong positive correlation.

So, the variable, number of bedrooms has stronger positive correlation and the variable

distance has the weakest correlation with dependent variable selling price.

5 d)

ANOVA

Model Sum of Squares

df MeanSquare

F Sig.

1 Regression

5039337.369

3 1679779.123

12.266 .000

Residual 7121257.7 52 136947.26

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01 3

Total 12160595.070

55

a Predictors: (Constant), Number of Bedrooms, Size of the Home in Square Feet, Distance


Global test:

Step 1: Ho: 1= 2= 3=0

H1: O /not all s are same.

Step 2: level of significance 0.05. (As not mentioned)

Step 3:

. ANOVAModel Sum of

Squaresdf Mean

SquareF Sig.

1 Regression

5039337.369

3 1679779.123

12.266 .000

Residual 7121257.701

52 136947.263

Total 12160595.070

55

a Predictors: (Constant), Number of Bedrooms, Size of the Home in Square Feet, Distance


Step 4: Reject if Ho if significant value (P value)


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Coefficients

Unstandardized

Coefficients

Standardized

Coefficients

t Sig.


1 (Constant) 930.282 542.946 1.713 .093Size of theHome inSquare

Feet

.636 .192 .353 3.309 .002

Distance -34.434 9.895 -.401 -3.480 .001

Number ofBedrooms

193.224 111.374 .199 1.735 .089

a Dependent Variable: Selling Price in TK. 000 (Thousand)

ForSize of the Home in Square Feet

Step 1: Ho: 1=0

H1: 1 O

Step 2: level of significance 0.05. ( As not mentioned)

Step 3:

. CoefficientsUnstandar

dizedCoefficients

Standardiz

edCoefficients

t Sig.


1 (Constant) 930.282 542.946 1.713 .093


Feet

.636 .192 .353 3.309 .002



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Step 7: Interpretation:

As Ho rejected. And, 1 O. that means 1 has value so X1 has value too.Bothinfluences or effect Y. Here x1= significant variable.

ForDistance

Step 1: Ho: 2=0

H1: 2O

Step 2: level of significance 0.05. (As not mentioned)

Step 3:Coefficients

Unstandardized

Coefficients

Standardized

Coefficients

t Sig.


1 (Constant) 930.282 542.946 1.713 .093

Distance -34.434 9.895 -.401 -3.480 .001



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Step 3:

Coefficients

Unstandardized

Coefficient

s

Standardized

Coefficient

s

t Sig.


Number ofBedrooms

193.224 111.374 .199 1.735 .089

Step 4: Reject if Ho if significant value (P value) .05So Ho Accepted. So, 3=O.

Step 7: Interpretation

As, Ho Accepted and, 3 =O. that means 3 has no value so X2 has no value. Both dont

influence or affect Y. Here x3= Insignificant variable

I would consider deleting any of theses variables. I would delete 3rd variable (Number ofbedrooms) as here x is insignificant variable and dont effect Y.

Now the linear equation will be:Y= a+1X1+ 2X2

==930.282+636+-34.434

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shajib final 2

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