Please answer Q3

The MidwestSales data set:

1 360000 3032 4 4 1 2 0 1972 2 1 22221 0 2 340000 2058 4 2 1 2 0 1976 2 1 22912 0 3 250000 1780 4 3 1 2 0 1980 2 1 21345 0 4 205500 1638 4 2 1 2 0 1963 2 1 17342 0 5 275500 2196 4 3 1 2 0 1968 2 7 21786 0 6 248000 1966 4 3 1 5 1 1972 2 1 18902 0 7 229900 2216 3 2 1 2 0 1972 2 7 18639 0 8 150000 1597 2 1 1 1 0 1955 2 1 22112 0 9 195000 1622 3 2 1 2 0 1975 3 1 14321 0 10 160000 1976 3 3 0 1 0 1918 3 1 32358 0 11 190000 2812 7 5 0 2 1 1966 3 7 56639 0 12 559000 2791 3 4 1 3 0 1992 1 1 30595 0 13 535000 3381 5 4 1 3 0 1988 1 7 23172 0 14 525000 3459 5 4 1 2 0 1978 1 5 35351 0 15 299900 2090 3 3 1 2 0 1987 2 1 24025 0 16 527000 3232 5 5 1 2 0 1984 2 6 21445 0 17 169900 1502 2 2 1 2 0 1956 2 1 28958 0 18 335250 2747 3 4 1 2 0 1993 2 7 22241 0 19 323900 2890 4 3 1 2 0 1954 2 7 41992 0 20 200000 1825 3 3 1 2 0 1957 2 1 30266 0 21 211000 1578 4 3 1 2 0 1986 2 2 18829 0 22 212000 1763 3 3 1 2 0 1959 2 1 24726 0 23 245000 2517 4 3 1 2 0 1965 2 1 23261 0 24 140400 1872 3 2 1 2 0 1985 2 3 24017 0 25 295000 3266 3 3 1 2 0 1908 2 6 24881 0 26 170900 2020 1 2 1 1 0 1956 2 1 21385 0 27 229000 2164 4 2 1 2 0 1965 2 1 28291 0 28 218500 2080 3 2 1 2 1 1959 2 1 14752 0 29 160000 2208 2 2 1 2 0 1985 2 7 8058 0 30 259000 3048 6 4 1 3 0 1960 2 7 29307 0 31 164500 1460 3 2 1 2 0 1978 2 1 9999 0 32 280000 2540 3 2 0 2 0 1940 2 5 42428 0 33 154000 2208 2 2 1 2 0 1985 2 7 6746 0 34 272000 2560 4 2 1 3 0 1977 2 5 36100 0 35 180000 2061 4 2 0 2 0 1958 2 1 20138 0 36 157500 1980 3 2 1 2 0 1957 2 1 32519 0 37 242500 3308 5 4 1 2 0 1928 2 5 47323 0 38 182000 2616 5 3 0 2 0 1955 3 5 11123 0 39 178000 1460 4 2 1 2 0 1961 3 1 27095 0 40 171900 1580 2 1 0 1 0 1951 3 4 12417 0 41 165500 1460 3 2 1 2 0 1960 3 1 22493 0 42 183500 1540 3 2 1 2 0 1992 3 3 15801 0 43 135000 1388 2 1 0 2 0 1951 3 1 26106 0 44 175000 1624 3 2 1 2 0 1948 3 1 39219 0 45 149500 1580 2 1 1 2 0 1966 3 1 11166 0 46 177500 1820 3 2 1 2 0 1960 3 1 22104 0 47 155000 1733 4 1 1 1 0 1936 3 4 22398 0 48 145000 1896 3 2 0 2 0 1925 3 6 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7 16640 0 120 367000 2940 4 7 1 2 0 1988 1 7 22003 0 121 470000 3430 3 4 1 2 1 1966 1 7 25018 0 122 393000 2472 4 4 1 3 0 1987 1 1 21784 0 123 530000 2878 4 4 1 3 0 1992 1 1 68351 0 124 400000 2537 3 3 1 2 0 1993 1 1 11053 0 125 403500 3858 4 4 1 3 0 1987 1 7 22224 0 126 550000 2742 3 3 1 3 0 1991 1 1 22306 0 127 380000 3460 5 4 1 2 0 1972 1 1 18571 0 128 500000 3836 5 4 1 3 0 1982 1 5 48465 0 129 465000 4453 7 5 1 2 0 1974 1 7 15595 0 130 451500 4080 5 4 1 3 0 1983 1 7 22134 0 131 336000 3301 3 4 1 2 0 1977 1 3 18741 0 132 550000 3828 4 5 1 2 1 1975 1 1 17051 0 133 450000 2973 4 3 1 2 0 1980 2 7 21999 0 134 440000 2821 5 4 1 2 1 1962 2 1 32914 0 135 515000 2950 5 3 1 2 0 1969 2 1 21598 0 136 415000 2362 3 3 1 2 0 1977 2 3 21604 0 137 380000 3092 3 4 1 2 0 1978 2 3 20081 0 138 489500 2866 4 4 0 2 0 1982 2 7 22424 0 139 478000 3369 5 4 1 3 0 1981 2 7 21161 0 140 460000 3068 4 4 1 3 0 1988 2 7 18289 0 141 379900 2380 3 3 1 3 0 1998 2 1 21999 0 142 390000 2225 2 3 1 3 0 1997 2 1 38722 0 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2 0 1969 2 7 18190 0 190 285400 2460 5 4 1 2 0 1979 2 7 27492 0 191 409000 3566 4 4 1 2 0 1976 2 7 18044 0 192 333000 2692 5 4 1 3 0 1984 2 7 22020 0 193 362000 2958 5 4 1 3 0 1987 2 7 45200 0 194 387500 3164 4 4 1 2 1 1966 2 7 23856 0 195 239000 2058 3 3 1 2 0 1969 2 2 21046 0 196 299900 2717 3 4 1 2 0 1983 2 7 22083 0 197 335000 2920 4 3 1 3 0 1987 2 7 22434 0 198 275000 2554 5 3 1 2 0 1960 2 7 21820 0 199 328000 2805 3 4 1 2 0 1988 2 7 22582 0 200 333000 2736 4 3 1 2 1 1979 2 7 29591 0 201 397000 3516 5 7 1 3 0 1996 2 7 34795 0 202 374800 3536 6 4 1 2 1 1978 2 7 19997 0 203 520000 2138 5 3 1 3 0 1956 2 1 86830 0 204 325000 2718 4 4 1 3 0 1978 2 6 22842 0 205 295000 2178 5 3 1 2 0 1958 2 1 25891 0 206 415000 3152 5 4 1 2 0 1980 2 6 24446 0 207 224900 2611 3 3 1 2 0 1987 2 7 6924 0 208 265000 2060 4 3 1 2 0 1981 2 2 13091 0 209 299900 2448 4 4 1 3 0 1979 2 7 26790 0 210 390000 4050 6 5 1 2 1 1966 2 7 18262 0 211 271000 2414 3 3 1 2 0 1914 2 7 24357 0 212 330000 3072 4 3 1 2 0 1966 2 7 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2 2 0 2 0 1951 3 1 29199 0 446 350000 2981 5 4 1 2 0 1950 3 6 49756 0 447 130000 1412 2 1 0 1 0 1940 3 1 16752 0 448 167900 2180 4 2 0 2 0 1948 3 3 15001 0 449 184900 1704 2 2 1 2 0 1954 3 1 16759 0 450 178000 1600 3 2 1 2 0 1957 3 3 15090 0 451 111000 1276 3 2 0 1 0 1951 3 1 11554 0 452 207000 1666 4 2 0 1 0 1954 3 1 39523 0 453 190000 1760 3 2 1 2 0 1974 3 2 20193 0 454 230000 1836 3 2 0 2 0 1946 3 1 46339 0 455 165000 1636 3 1 0 2 0 1953 3 1 20125 0 456 210000 1748 3 2 1 2 0 1957 3 1 14512 0 457 226000 2556 4 2 0 2 0 1923 3 6 36276 0 458 149900 1511 4 1 1 1 0 1954 3 1 14821 0 459 155000 1524 3 2 1 2 0 1958 3 1 21875 0 460 219900 1821 4 2 1 2 0 1956 3 1 16696 0 461 132000 1596 1 1 0 0 0 1940 3 1 28357 0 462 195000 2392 4 2 0 2 0 1960 3 1 30265 0 463 155900 1748 2 1 1 2 0 1956 3 1 16231 0 464 119900 1384 2 1 0 0 0 1949 3 1 30002 0 465 175000 1628 3 1 1 2 1 1957 3 1 17069 0 466 304000 1911 4 2 1 2 0 1953 3 1 86248 0 467 190000 1624 4 3 0 1 0 1959 3 3 15002 0 468 229100 1956 3 2 1 2 1 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31657 0 492 158000 1604 3 2 1 1 0 1960 3 1 23534 0 493 175000 2035 4 2 1 3 0 1962 3 7 20131 0 494 147000 1534 3 2 0 1 0 1955 3 3 15361 0 495 155000 1624 2 2 1 2 0 1955 3 1 16721 0 496 150000 1700 4 2 1 1 0 1954 3 1 15391 0 497 165000 1630 3 2 1 2 0 1978 3 2 24963 0 498 147000 1526 3 2 1 1 0 1957 3 1 15007 0 499 146250 1672 3 1 1 2 0 1949 3 1 22617 0 500 177500 1588 4 2 1 2 0 1980 3 2 21925 0 501 153650 1752 4 2 1 2 0 1950 3 6 9126 0 502 199500 1674 4 2 0 2 0 1947 3 1 33237 0 503 186000 1980 3 1 0 1 0 1927 3 6 47679 0 504 139900 1396 1 1 0 2 0 1950 3 1 25879 0 505 160000 1178 1 1 0 2 0 1959 3 1 9941 0 506 125000 1263 2 2 0 0 0 1955 3 1 12357 0 507 359900 2377 5 2 1 2 0 1937 3 6 51005 0 508 184500 1304 3 1 1 2 0 1951 3 1 21305 0 509 155000 1340 3 1 0 0 0 1952 3 1 5666 0 510 150000 1559 2 1 0 2 0 1952 3 1 23999 0 511 146000 1412 1 2 1 0 0 1920 3 1 4560 0 512 129000 1198 2 2 1 2 0 1925 3 1 20918 0 513 145000 1424 2 1 1 2 0 1947 3 1 16414 0 514 200000 1370 4 1 0 1 0 1925 3 4 8000 0 515 149900 1584 3 2 1 2 0 1957 3 1 13514 0 516 132000 1567 2 1 1 1 0 1934 3 4 12249 0 517 136900 1409 2 1 0 1 0 1951 3 1 28421 0 518 137000 1655 2 1 0 1 0 1935 3 1 54651 0 519 185000 1944 3 2 1 2 0 1939 3 6 17999 0 520 133500 1922 3 1 0 2 0 1950 3 1 14805 0 521 124000 1480 3 2 1 2 0 1953 3 1 28351 0 522 95500 1184 2 1 0 1 0 1951 3 1 14786 0

g. What would happen to the interval from part f. if the confidence level is decreased to 90%? Explain in a sentence or two. h. Run a summary of your dataset (in R, this is: summary(dataset) ). Would it make sense to predict the sale price of a house that is 8500 square feet?i. 'What would happen to the interval from part f. if the condence level is increased to 100%? Explain in a sentence or two. j. What is the estimate of 0'5? Interpret this quantity in context of the problem. k. Say we have two houses. House one is 1500 sqft (call this X1) and house two is 3500 sqft (X2). Does it make sense for both these houses to have the same estimate of are? Explain in context of the problem. 3. This question will use the MidwestSales data set that is on the class website. This dataset involves houses being sold in the midwest. The response variable is the price the house was sold (in dollars) and explanatory variables such as the square footage of the house, the number of bedroom, the year the house was built, etc. Run the following lines to import the dataset and then to give names to the variables. Remember to replace the "./MidwestSales.txt", in the read.table call with your own path to where you saved the dataset. Say you named the dataset "MidwestSales": # Import MidWestSales dataset MidwestSales = read. table(". /MidwestSales. txt", fill=TRUE, header=FALSE) # This dataset does not have names, so we will add names to the variables names (MidWestSales)=c("id", "price", "sqft", "bed", "bath", "ac", "garage", "pool", "year", "quality", "style", "lot","hwy") a. Fit a linear model where the square footage of the house is used to predict the sale price. (X=sqft and Y=price). Write the estimated regression equation. b. Interpret the estimate of the slope. c. Test whether square footage has a significant linear relationship with price. Use a = 0.05 level of significance. Write the null and alternative hypothesis, state the test statistic and p-value, and make a conclusion. d. Now test whether square footage has a significant positive linear relationship with price. Use a = 0.05 level of significance. Write the null and alternative hypothesis, state the test statistic and p-value, and make a conclusion. e. Find and interpret a 95% confidence interval for the mean price when sqft=2000. f. Find and interpret a 95% prediction interval for the price when sqft-2000