Question

In: Math

Price Bedroom Bathroom Cars SQ FT 298,000 3 2.5 0 1,566 319,900 3 2.5 0 2,000...

Price Bedroom Bathroom Cars SQ FT
298,000 3 2.5 0 1,566
319,900 3 2.5 0 2,000
354,000 3 2 2 0
374,900 4 2.5 0 2,816
385,000 4 2 0 0
389,000 3 2.5 0 2,248
399,000 4 3 0 2,215
415,000 3 2.5 0 3,188
444,900 3 2 0 2,530
450,000 3 2 0 1,967
465,000 4 3 0 2,564
340,000 4 2.5 0 2,293
275,000 3 2.5 2 1,353
425,000 3 2 0 1,834
250,000 3 2.5 0 5,837
450,000 3 2.5 0 9,060
390,000 3 3.5 0 1,002
269,000 3 2.5 0 1,680
425,000 3 2.5 2 4,356
425,000 2 2.5 2 2,993
425,000 3 3 0 4,356
429,900 5 3.5 1 2,154
400,000 3 2.5 2 1,846
399,900 3 2 1 2,018
388,990 4 4 0 2,295
  1. Plz do all the calculations on excel n show the excel files.
  2. Construct and interpret a correlation matrix for your data.
  3. Show the step wise process of determining the best regression model to predict PRICE Anova. EXPLAIN the process as you move from the full model to your final model.
  4. Using your final model, select values for the independent variables and predict the house’s sales price.

Solutions

Expert Solution

data -> data analysis -> correlation

Price Bedroom Bathroom Cars SQ FT
Price 1
Bedroom 0.1163 1
Bathroom 0.0693 0.4544 1
Cars -0.0119 -0.2773 -0.1439 1
SQ FT 0.1825 -0.1648 0.0818 -0.1522 1

with Price, there is weak correlation with every independent variable

SQ FT has highest correlation with Price

Bathroom and Bedroom has correlation 0.4544

data -> data analysis -> regression

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.2449
R Square 0.0600
Adjusted R Square -0.1280
Standard Error 63973.0562
Observations 25
ANOVA
df SS MS F Significance F
Regression 4 5222651649.4394 1305662912.3598 0.3190 0.8619
Residual 20 81851038446.5607 4092551922.3280
Total 24 87073690096.0000
Coefficients Standard Error t Stat P-value Lower 95%
Intercept 309980.8034 90752.3457 3.4157 0.0027 120674.7275
Bedroom 17945.0381 25574.4249 0.7017 0.4910 -35402.2774
Bathroom -2595.9465 28990.2834 -0.0895 0.9295 -63068.6180
Cars 5114.6350 16897.8149 0.3027 0.7653 -30133.5893
SQ FT 7.3638 7.4722 0.9855 0.3362 -8.2230

see the column p-value

we observe that all independent variable has p-value > 0.05

hence they all are insignificant

lowest p-value is of SQ Ft

so we just include this

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.182509324
R Square 0.033309653
Adjusted R Square -0.008720362
Standard Error 60495.52468
Observations 25
ANOVA
df SS MS F Significance F
Regression 1 2900394438 2900394438 0.792520615 0.382556796
Residual 23 84173295658 3659708507
Total 24 87073690096
Coefficients Standard Error t Stat P-value Lower 95%
Intercept 368173.8051 21041.84324 17.49722213 8.72146E-15 324645.4359
SQ FT 5.970685713 6.706855155 0.890236269 0.382556796 -7.903501245

y^ = 368173.8051 + 5.9707 SQ FT


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