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HouseID 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 Age 7 8 5 7 3 10 5 5 7 7 4 9 8 5 6 7 8 6 3 9 8 6 7 4 7 5 2 6 7 6 7 5 10 9 6 8 9 9 8 8 7 6 6 4 5 8 11 4 3 9 6 7 6 Size 1580 1744 1863 1824 1924 1707 1898 2063 1641 1524 2144 1518 1645 2741 1718 1713 2240 1809 1588 1941 1783 2186 2018 2375 1801 2266 1891 2514 1738 2091 2495 1551 1814 1822 2289 2080 1758 2299 2190 1671 1544 1331 1386 2219 1793 1812 1499 1766 2060 1529 1276 2086 1395 Bedrooms 3 3 3 4 4 4 3 4 3 3 3 2 3 4 3 3 4 3 4 3 4 4 4 4 4 3 3 4 3 3 4 3 4 3 4 3 3 3 3 3 3 2 3 4 3 3 3 3 3 3 2 3 2 Price 132.0 123.9 159.1 126.0 128.3 145.4 126.1 128.4 147.4 121.5 167.7 109.2 132.6 212.3 111.8 119.6 162.0 145.1 124.4 129.8 127.4 141.8 131.3 164.2 127.9 158.8 131.2 173.3 121.4 170.0 185.6 111.4 134.9 117.1 186.8 141.4 137.6 181.5 139.2 137.6 137.4 93.7 86.5 153.0 129.4 145.5 124.2 134.6 162.5 109.1 97.9 146.8 95.1 Price Size Bedrooms Age House Price ($1,000) House Size (Square Feet) Bedrooms Age (years) SUMMARY OUTPUT: Dependent Variable is Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA Regression Residual Total Intercept Size Bedrooms Age 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 4 8 7 8 5 2 7 6 6 6 5 3 8 6 5 9 10 4 5 4 4 9 10 2 8 9 5 5 2 3 6 9 6 6 5 5 4 8 9 4 4 2 7 8 8 7 5 1409 2009 1894 1190 1811 1689 1690 1685 1588 1730 1951 2040 1749 1111 1775 1478 2125 1596 1610 1724 1713 1490 1881 1868 2257 1614 1775 1770 2213 1743 2068 1705 1788 2334 1579 1478 2042 2263 1659 1978 1598 2523 1846 2292 1872 1954 1679 2 3 4 2 3 3 3 3 3 3 3 3 3 2 4 2 3 3 3 2 3 3 3 3 4 4 3 3 3 3 3 3 4 4 2 2 3 3 3 4 3 4 3 3 3 3 3 116.0 155.3 144.1 88.8 152.6 146.5 136.4 125.2 127.6 143.6 158.8 139.9 141.2 86.7 116.2 100.7 171.8 135.1 139.5 151.4 122.5 115.3 152.4 162.0 163.6 145.3 143.7 129.3 175.1 152.2 162.8 126.7 138.5 180.1 103.0 105.1 167.2 158.8 122.5 131.1 125.2 197.9 143.5 163.2 153.8 146.1 118.4 e (Square Feet) Y OUTPUT: Dependent Variable is Price egression Statistics 0.861 0.741 0.733 12.513 100 df 3 96 99 Coefficients 17.953 0.069 -1.458 -0.385 2 3 5 SS MS F Significance F 43031.86011 14343.95 91.61587 4.57688E-28 15030.36029 156.5663 58062.2204 Standard Error 9.364 0.005 2.667 0.602 t Stat 1.917 13.455 -0.547 -0.640 P-value 5.82% 0.00% 58.58% 52.40% Lower 95% -0.634 0.059 -6.752 -1.581 Upper 95% 36.539 0.080 3.836 0.810 HouseID Bedrooms 1 3 2 3 3 3 4 4 5 4 6 4 7 3 8 4 9 3 10 3 11 3 12 2 13 3 14 4 15 3 16 3 17 4 18 3 19 4 20 3 21 4 22 4 23 4 24 4 25 4 26 3 27 3 28 4 29 3 30 3 31 4 32 3 33 4 34 3 35 4 36 3 37 3 38 3 39 3 40 3 41 3 42 2 43 3 44 4 45 3 46 3 47 3 48 3 49 3 50 3 51 2 52 3 53 2 54 2 Price 132.0 123.9 159.1 126.0 128.3 145.4 126.1 128.4 147.4 121.5 167.7 109.2 132.6 212.3 111.8 119.6 162.0 145.1 124.4 129.8 127.4 141.8 131.3 164.2 127.9 158.8 131.2 173.3 121.4 170.0 185.6 111.4 134.9 117.1 186.8 141.4 137.6 181.5 139.2 137.6 137.4 93.7 86.5 153.0 129.4 145.5 124.2 134.6 162.5 109.1 97.9 146.8 95.1 116.0 Price Price ($1,000) of each house Bedrooms Number of Bedrooms in each house 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 3 4 2 3 3 3 3 3 3 3 3 3 2 4 2 3 3 3 2 3 3 3 3 4 4 3 3 3 3 3 3 4 4 2 2 3 3 3 4 3 4 3 3 3 3 3 155.3 144.1 88.8 152.6 146.5 136.4 125.2 127.6 143.6 158.8 139.9 141.2 86.7 116.2 100.7 171.8 135.1 139.5 151.4 122.5 115.3 152.4 162.0 163.6 145.3 143.7 129.3 175.1 152.2 162.8 126.7 138.5 180.1 103.0 105.1 167.2 158.8 122.5 131.1 125.2 197.9 143.5 163.2 153.8 146.1 118.4 Fish Wt (oz) 9.3 10.3 12.1 11.7 9.8 9.8 11.0 9.5 7.1 9.8 9.8 8.3 10.1 9.0 10.3 8.9 10.7 10.6 8.7 9.3 10.1 9.5 9.6 10.2 10.8 10.4 8.8 8.7 9.4 9.3 7.6 9.8 10.3 10.0 9.8 10.7 8.8 9.2 10.8 9.3 11.0 7.5 9.2 10.2 9.0 8.1 9.1 10.1 9.9 11.0 9.2 9.4 9.4 9.7 8.3 9.7 10.4 10.7 10.6 9.1 9.7 An auto loan company is interested in the difference in credit history for young and old bo A sample of 1000 loans from younger borrowers found 3.0% defaulted and 500 loa Old Young Defualt Pct 6.0% 3.0% Number of Borrowers 500 1000 defaulted and 500 loans from older borrowers found 6.0% defaulted. Name:_______________________________ Stat 2103 - Take Home Final Exam due Wednesday Dec 12 11:59pm The data for these problems are on the Excel sheet for Week 15 on Canvas. You can show your work in the Excel sheet. Rename the Excel file with your last name and upload it via the Canvas link on Week 15. Type your answers on this sheet. Upload it before midnight on Wed Dec 12. (1) (6 pts) An auto loan company is interested in the difference in credit history for young and old borrowers. A sample of 1000 loans from younger borrowers found 3.0% defaulted and 500 loans from older borrowers found 6.0% defaulted. a. Construct a 95% confidence interval around the difference default rates for old and young borrowers. What are the lower and upper bounds of this confidence interval? b. Is there a statistically significant difference in the default rates between old and young borrowers at the 5% significance level? (2) (9 pts) Use the data on the sheet “FishWt”. This data was sampled from a certain population of fish. A biologist wants to test the research hypothesis that this fish population has a mean weight below 10 oz. Test the research hypothesis that sales increase during the campaign at the 5% significance level. a. What are the null and alternative hypotheses? b. What is the appropriate p-value? c. Using this data, can the biologist infer at the 1% significance level that the fish population has an average weight below 10 oz? State your conclusion. (3) (15 pts) Use the data on the sheet “Bedrooms” to create a simple regression model. Use Price as the dependent (Y) variable and Bedrooms as the independent (X) variable. a. What is the slope and intercept for this model? What the units of the slope? b. Use your simple regression model to predict the price of a 4 bedroom home? c. What is the residual for HouseID #1? d. What is the p-value for the hypothesis the hypothesis that slope between Bedrooms and Price is zero? e. Can you infer at the 1% significance level that Bedrooms is a statistically significant predictor of price? Explain. For the remaining questions, use the sheet “HouseData3X” This sheet contains data on the same 100 homes and the results of the Excel Regression macro using price as the dependent variable and three predictor variables. It also includes an explanation and units for each variable. (4) (10 pts) Refer to the multiple regression model using Size, Bedrooms and Age to predict Price. a. Which predictor variables are statistically significant at the α=10% level? b. What is the slope and p-value of the Bedrooms variable? How and why did these two change from question 3? c. What percentage of the variability in Price is explained by this model?
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Name:_______________________________

Stat 2103 - Take Home Final Exam due Wednesday Dec 12 11:59pm
The data for these problems are on the Excel sheet for Week 15 on Canvas.
You can show your work in the Excel sheet. Rename the Excel file with your last name and upload it via
the Canvas link on Week 15.
Type your answers on this sheet. Upload it before midnight on Wed Dec 12.
(1) (6 pts) An auto loan company is interested in the difference in credit history for young and old borrowers.
A sample of 1000 loans from younger borrowers found 3.0% defaulted and 500 loans from older
borrowers found 6.0% defaulted.
a. Construct a 95% confidence interval around the difference default rates for old and young
borrowers. What are the lower and upper bounds of this confidence interval?
The 95% confidence interval of the difference in default rates for old and young is:
𝟎. 𝟎𝟎𝟔𝟕 < 𝒑𝒐𝒍𝒅 − 𝒑𝒚𝒐𝒖𝒏𝒈 < 𝟎. 𝟎𝟓𝟑𝟑
b. Is there a statistically significant difference in the default rates between old and young
borrowers at the 5% significance level?
Since the 95% confidence interval does not include 0, at 5% significance level, there is
statistically significant difference in the default rates between old and young borrowers.
(2) (9 pts) Use the data on the sheet “FishWt”. This data was sampled from a certain population of fish. A
biologist wants to test the research hypothesis that this fish population has a mean weight below 10
oz. Test the research hypothesis that sales increase during the campaign at the 5% significance level.
a. What are the null and alternative hypotheses?
Null hypothesis:
Alternative hypothesis:

𝐇𝟎 : 𝛍𝐰𝐞𝐢𝐠𝐡𝐭 = 𝟏𝟎
𝐇𝐚 : 𝛍𝐰𝐞𝐠𝐡𝐭 < 𝟏𝟎

b. What is the appropriate p-value?
The p-value of the left-tailed t-test is 0.0058
c. Using this data, can the biologist infer at the 1% significance level that the fish population has
an average weight below 10 oz? State your conclusion.
At 1% significance level, the p-value (0.0058) is less than alpha (i.e. 𝜶 = 𝟎. 𝟎𝟏). We reject the
null hypothesis and accept the alternative hypothesis. In conclusion, there is sufficient
evidence to support the alternative hypothesis that the mean weight is less than 10 oz.

(3) (15 pts) Use the data on the sheet “Bedrooms” to create a simple regression model. Use Price as the

dependent (Y) variable and Bedrooms as the independent (X) variable.
a. What is the slope and intercept for this model? What the units of the slope?
The slope is: ...


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