Seth Satterfield - Submission Form - Relationship Significance Testing Lab + HW

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Kennesaw State University *

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Apr 3, 2024

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Name: RELATIONSHIP SIGNIFICANCE TESTING LAB AND HOMEWORK SUBMISSION FORM Please organize your analysis in the appropriate space below. Do not change the order, this is to help expedite the grading process and get your feedback to you as quickly as possible. Students must submit both this word document and the excel workbook. Analysis in the workbook and the word document should be consistent. No credit will be awarded if the Excel file is not submitted. ALL TABLES AND GRAPHS SHOULD BE NEATLY FORMATTED, ORGANIZED, AND PASTED AS PICTURES IN THE WORD DOCUMENT. INTEPRETATIONS AND HYPOTHESIS STATEMENTS SHOULD BE WELL WRITTEN WITH PROPER GRAMMAR AND SPELLING Regression Test 1 Table and Plot Output Regression Statistics Multiple R 0.694537 R Square 0.482381 Adjusted R Square 0.482002 Standard Error 50976.19 Observations 1367 Coefficients Standard Error t Stat P-value Lower 95.0% Upper 95.0% Intercept 26616.70084 4736.6295 26 5.619333 472 0.00 17324.83 846 35908.56 322 Living Area 105.4835451 2.9575226 01 35.66618 395 0.00 99.68176 292 111.2853 274 Regression Test 1 Hypothesis Statements and Interpretations Null: There is no relationship between living area and sales price. (Slope = 0) Alt: The is a statistically significant relationship between living area and sales price (Slope ≠ 0) 1

Multiple R: The correlation coefficient of 0.695 indicates that there is a strong relationship between living area and sale price. R Square: The coefficient of determination indicates that 48.2% (0.482) of the variation is sale price can be explained by the amount of living area square footage. P-value and Conclusion: Since the p-value of 0.000 is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is a statistically significant relationship between living area and sale. Regression Test 2 Table and Plot Output Regression Statistics Multiple R 0.490779376 R Square 0.240864396 Adjusted R Square 0.240308253 Standard Error 61733.67415 Observations 1367 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 166896.373 1959.497035 85.17306742 0 163052.421 170740.3251 163052.421 170740.3251 MasonryVeneer Area 201.1049047 9.663394571 20.81100003 9.128E-84 182.1481904 220.0616189 182.1481904 220.0616189 Regression Test 2 Hypothesis Statements and Interpretations Null: There is no relationship between masonry veneer area and sales price. (Slope = 0) Alt: The is a statistically significant relationship between masonry veneer area and sales price (Slope ≠ 0) Multiple R: The correlation coefficient of 0.491 indicates that there is a strong relationship between masonry veneer area and sale price. R Square: The coefficient of determination indicates that 24.1% (0.241) of the variation is sale price can be explained by the amount of masonry veneer area square footage. P-value and Conclusion: Since the p-value of 0.000 is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is a statistically significant relationship between masonry veneer area and sale. Regression Test 3 Table and Plot Output 2

Regression Statistics Multiple R 0.57698284 R Square 0.332909198 Adjusted R Square 0.332420487 Standard Error 57870.19174 Observations 1367 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 72189.96977 4713.806502 15.31458063 5.6416E-49 62942.8794 81437.06015 62942.8794 81437.06015 Full Baths 56455.1414 2163.050968 26.09977399 3.7908E-122 52211.8769 60698.40589 52211.8769 60698.40589 Regression Test 3 Hypothesis Statements and Interpretations Null: There is no relationship between full baths and sales price. (Slope = 0) Alt: The is a statistically significant relationship between full baths and sales price (Slope ≠ 0) Multiple R: The correlation coefficient of 0.577 indicates that there is a strong relationship between full baths and sale price. R Square: The coefficient of determination indicates that 33.2% (0.332) of the variation is sale price can be explained by the amount of full baths. P-value and Conclusion: Since the p-value of 0.000 is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is a statistically significant relationship between full baths and sale. Regression Test 4 Table and Plot Output Regression Statistics Multiple R 0.644035071 R Square 0.414781172 Adjusted R Square 0.414352441 Standard Error 54202.78354 Observations 1367 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 65394.78733 4212.769828 15.52299081 3.6132E-50 57130.58232 73658.99234 57130.58232 73658.99234 Garage Car Capacity 66717.50565 2144.979288 31.10403258 5.2441E-161 62509.69243 70925.31887 62509.69243 70925.31887 3

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Regression Test 4 Hypothesis Statements and Interpretations Null: There is no relationship between garage car capacity and sales price. (Slope = 0) Alt: The is a statistically significant relationship between garage car capacity and sales price (Slope ≠ 0) Multiple R: The correlation coefficient of 0.664 indicates that there is a strong relationship between garage car capacity and sale price. R Square: The coefficient of determination indicates that 41.5% (0.415) of the variation is sale price can be explained by the amount of garage space for cars. P-value and Conclusion: Since the p-value of 0.000 is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is a statistically significant relationship between garage car capacity and sale ANOVA Test 1 Table Output Groups Count Sum Average Variance Concrete Block 570 88344985 $154,991 1817271213 Poured Concrete 675 151697449 $224,737 5725162117 Slab Stone 122 17280202 $141,641 1369292835 Source of Variation SS df MS F P-value F crit Between Groups 1.79416E+12 2 8.97082E+11 241.8950704 1.21982E-90 3.002321399 Within Groups 5.05847E+12 1364 3708556466 Total 6.85263E+12 1366 ANOVA Test 1 Hypothesis Statements and Interpretations Null: There is no relationship between Foundation Type and sales price. (Mean Poured Concrete = Mean Cinder Block = Mean Slab) Alt: The is a statistically significant relationship between Foundation Type and sales price (At least one mean is different) P-value and Conclusions: Since the p-value of 0.000 is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is a statistically significant relationship between foundation type and sale price. One 4

thing to note is that there are unequal variances between the groups and we do not know if one mean is significantly different or is all means are different Pairwise T-Test 1 Table Output Poured Concrete Concrete Block Mean $224,737 $154,991 Variance 5725162116.68 1817271213 Observations 675.00 570 Hypothesized Mean Difference 0.00 df 1093.00 t Stat 20.42 P(T<=t) one-tail 0.00 t Critical one-tail 1.65 P(T<=t) two-tail 0.00 t Critical two-tail 1.96 Pairwise T-Test 1 Interpretations Null: There is no difference in the mean sale price for homes with poured concrete and concrete block. (Mean Poured Concrete = Mean Cinder Block) (Mean Poured Concrete - Mean Cinder Block = 0) Alt: The is a statistically significant difference in the mean sale price for home with poured concrete and concrete block. P-value and Conclusions: Since the p-value of 0.000 is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is a statistically significant relationship between foundation type and sale price for homes with poured concrete compared to cinder block. Pairwise T-Test 2 Table Output Concrete Block Slab Stone Mean 154991.2018 141641 Variance 1817271213 1369292835 Observations 570 122 Hypothesized Mean Difference 0 df 196 t Stat 3.516633472 P(T<=t) one-tail 0.000271506 t Critical one-tail 1.652665059 P(T<=t) two-tail 0.000543011 t Critical two-tail 1.972141222 5

Pairwise T-Test 2 Interpretations Null: There is no difference in the mean sale price for homes with slab and concrete block. (Mean Slab = Mean Cinder Block) (Mean Cinder Block - Mean Slab = 0) Alt: The is a statistically significant difference in the mean sale price for home with slab and concrete block. P-value and Conclusions: Since the p-value of 0.000 is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is a statistically significant relationship between foundation type and sale price for homes with cinder block and slab. Pairwise T-Test 3 Table Output Poured Concrete Slab Stone Mean $224,737 $141,641 Variance 5725162116.68 1369292835 Observations 675.00 122 Hypothesized Mean Difference 0.00 df 338.00 t Stat 18.72 P(T<=t) one-tail 0.00 t Critical one-tail 1.65 P(T<=t) two-tail 0.00 t Critical two-tail 1.97 Pairwise T-Test 3 Interpretations Null: There is no difference in the mean sale price for homes with poured concrete and concrete block. (Mean Slab = Mean Cinder Block) (Mean Cinder Block - Mean Slab = 0) Alt: The is a statistically significant difference in the mean sale price for home with slab and concrete block. P-value and Conclusions: Since the p-value of 0.000 is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is a statistically significant relationship between foundation type and sale price for homes with poured concrete and slab. ANOVA Test 2 Table Output Groups Count Sum Average Variance Split Level 233 35414225 $151,992 1780364242 1 Story 702 130575096 $186,004 4954085852 2 Story 429 90734315 $211,502 5622335132 2.5 Story 3 599000 $199,667 9120333333 6

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Source of Variation SS df MS F P-value F crit Between Groups 5.42175E+11 3 1.80725E+11 39.03492803 3.36386E-24 2.611431218 Within Groups 6.31046E+12 1363 4629830366 Total 6.85263E+12 1366 ANOVA Test 2 Hypothesis Statements and Interpretations Null: There is no relationship between House Style and sales price. (Mean Split Level = Mean 1 story = Mean 2 story = Mean 2.5 story) Alt: The is a statistically significant relationship between House Style and sales price (At least one mean is different) P-value and Conclusions: Since the p-value of 0.000 is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is a statistically significant relationship between House Style and sale price. 7