Using the data in the Excel file Demographics, apply the Excel Regression tool u

Question

Using the data in the Excel file Demographics, apply the Excel Regression tool using unemployment rate as the dependent variable and cost of living index as the independent variable.

a. Interpet all key regression results, hypothesis tests, and confidence intervals in the output

b. Analyze the residuals to detemine if the assumptions underlying the regression analysis are valid.

c. Use the standard residuals to detremine if any possible outliers exist

Demographic Data Unemployment Cost of Living Population Metropolitan Area State (July 1999) 1999 - US Avg = 100 (July 1999) ANCHORAGE AK 3.60% 125.90 257,808 BIRMINGHAM AL 2.70% 99.10 915,077 HUNTSVILLE AL 2.70% 95.20 343,418 MOBILE AL 3.60% 91.80 535,472 MONTGOMERY AL 2.90% 92.40 322,441 LITTLE ROCK AR 3.20% 87.20 559,074 PHOENIX AZ 2.60% 99.90 3,013,696 TUCSON AZ 2.30% 99.70 803,618 BAKERSFIELD CA 12.50% 106.10 642,495 FRESNO CA 13.80% 105.80 879,829 LOS ANGELES CA 6.30% 122.00 25,366,576 SACRAMENTO CA 4.10% 114.00 3,328,431 SAN DIEGO CA 3.20% 122.80 2,820,844 SAN FRANCISCO CA 2.50% 144.70 8,559,292 COLORADO SPRINGS CO 3.70% 96.80 499,994 DENVER CO 2.60% 105.30 4,417,908 PUEBLO CO 5.80% 92.50 136,987 HARTFORD CT 3.40% 121.80 1,147,504 WASHINGTON DC 2.90% 132.00 4,739,999 WILMINGTON DE 3.20% 108.10 571,420 FORT MYERS FL 4.40% 97.20 400,542 JACKSONVILLE FL 2.90% 95.40 1,056,332 MIAMI FL 6.70% 104.50 2,175,634 ORLANDO FL 2.90% 97.00 1,535,004 PENSACOLA FL 3.70% 93.60 403,384 TALLAHASSEE FL 3.10% 100.10 200,003 TAMPA FL 2.90% 97.80 2,278,169 WEST PALM BEACH FL 5.60% 104.70 1,049,420 ATLANTA GA 3.00% 97.40 3,857,097 COLUMBUS GA 4.40% 93.90 271,417 MACON GA 4.70% 95.10 321,586 DES MOINES A 1.80% 94.70 443,496 DUBUQUE A 2.60% 107.50 88,112 BOISE ID 3.30% 102.70 407,844 POCATELLO ID 4.50% 99.80 74,881 CHICAGO IL 4.00% 121.60 8,008,507 ROCKFORD IL 4.10% 103.60 358,640 SPRINGFIELD IL 3.60% 95.10 358,640 FORT WAYNE IN 2.40% 93.30 484,320 INDIANAPOLIS IN 2.30% 94.90 2 SOUTH SEND IN 2.40% 90.90 258,537 TOPEKA KS 4.30% 95.10 170,773 WICHITA KS 3.30% 94.80 548,714 LEXINGTON KY 1.90% 95.90 455,617 LOUISVILLE KY 2.70% 92.80 1,005,849 BATON ROUGE LA 3.70% 98.50 578,946 NEW ORLEANS LA 4.00% 94.50 1,305,479 SHREVEPORT LA 4.80% 94.90 377,673 BOSTON MA 2.20% 136.80 3,297,201 BALTIMORE MD 4.70% 102.30 2,491,254 DETROIT MI 2.80% 113.00 4,474,614 GRAND RAPIDS MI 2.50% 102.10 1,052,092 LANSING MI 2.10% 102.90 450,789 MINNEAPOLIS-ST.PAUL MN 1.50% 99.70 2,872,109 ROCHESTER MN 1.20% 97.50 119,077 COLUMBIA MO 1.40% 93.10 130,179 KANSAS CITY MO 3.20% 96.10 1,756,899 SPRINGFIELD MO 2.50% 94.50 308,332 ST. LOUIS MO 3.50% 97.40 2,569,029 JACKSON MS 2.80% 94.30 432,647 BILLINGS MT 3.80% 102.70 127,258 GREAT FALLS MT 5.70% 102.50 782,132 MISSOULA MT 5.20% 101.80 89,344 ASHEVILLE NC 3.30% 100.00 215,180 CHARLOTTE NC 5.00% 96.80 1,417,217 GREENSBORO-WNSTN-S NC 2.80% 97.50 1,179,384 RALEIGH NC 1.90% 97.30 1,106 WILMINGTON NC 4.20% 97.80 222,109 BISMARCK ND 1.80% 99.90 91,939 FARGO ND 1.10% 100.80 170,122 LINCOLN NE 1.40% 88.80 237,057 OMAHA NE 1.90% 92.30 698,875 CONCORD NH 2.30% 108.80 239,069 ATLANTIC CITY NJ 12.70% 132.60 337,635 ALBUQUERQUE NM 4.60% 102.80 678,820 LAS VEGAS NV 3.30% 105.60 1,381,086 RENO NV 2.80% 111.80 319,816 ALBANY NY 3.10% 109.70 869,474 BUFFALO NY 4.50% 97.30 1,142,121 NEW YORK NY 7.60% 226.50 20,196,649 ROCHESTER NY 3.50% 110.40 1,079,073 SYRACUSE NY 3.40% 102.90 732,920 AKRON OH 3.70% 96.30 689,435 CINCINNATI OH 3.20% 101.10 1,960,995 CLEVELAND OH 4.20% 106.00 2,221,181 COLUMBUS OH 2.50% 101.40 1,489,487 TOLEDO OH 4.60% 96.90 608,976 OKLAHOMA CITY OK 3.00% 90.20 1,046,283 TULSA OK 3.00% 89.40 786,117 EUGENE OR 5.10% 108.90 314,901 PORTLAND OR 4.30% 107.30 1,845,840 SALEM OR 5.50% 103.30 335,156 ALLENTOWN PA 4.40% 104.40 618,350 ERIE PA 4.70% 101.60 276,993 HARRISBURG PA 2.70% 104.90 618,375 PHILADELPHIA PA 4.00% 127.40 4,949,567 PITTSBURGH PA 4.31% 113.30 2,331,336 WILLIAMSPORT PA 5.10% 97.50 116,709 CHARLESTON SC 2.50% 95.20 552,803 COLUMBIA SC 1.80% 94.20 516,251 GREENVILLE SC 2.50% 95.20 929,565 RAPID CITY SO 2.40% 100.20 88,117 SIOUXFALLS SO 1.40% 96.60 164,481 KNOXVILLE TN 3.40% 93.80 672,087 MEMPHIS TN 3.20% 95.30 1,105,050 NASHVILLE TN 2.50% 91.70 1,171,755 ABILENE TX 3.40% 91.80 122,478 AMARILLO TX 3.10% 90.00 208,691 AUSTIN TX 2.40% 100.90 1,146,050 CORPUS CHRISTI TX 6.40% 93.60 387,105 DALLAS-FORT WORTH TX 2.90% 101.80 3,280,310 ELPASO TX 9.80% 95.00 701,908 HOUSTON TX 3.80% 96.80 4,010,969 SAN ANTONIO TX 3.20% 99.60 1,564,949 WACO TX 3.30% 92.10 204,244 SALT LAKE CITY UT 2.70% 100.90 1,275,076 NORFOLK VA 3.30% 100.50 1,562,635 RICHMOND VA 2.80% 102.00 961,416 ROANOKE VA 2.10% 93.00 277,741 BURLINGTON VT 1.90% 109.60 165,917 OLYMPIA WA 4.80% 103.40 205,459 SEATTLE WA 3.10% 119.70 2,334,934 SPOKANE WA 5.30% 106.70 409,736 YAKIMA WA 11.70% 102.60 220,785 GREEN BAY Wl 2.40% 97.00 216,522 LA CROSSE WI 2.50% 98.50 121,927 MILWAUKEE Wl 3.30% 107.50 1,462,422 CHARLESTON WV 4.40% 96.60 251,199 HUNTINGTON WV 5.80% 100.80 312,447 CASPER WY 5.00% 101.40 63,157 CHEYENNE WY 3.30% 95.00 78,877

Explanation / Answer

Ans:

The residuals (blunder terms) tackle positive qualities with little or extensive fitted values, and negative qualities in the center. The width of the disperse appears to be reliable, yet the focuses are not haphazardly scattered around the zero line from left to right. Utilizing lingering plots, you can survey whether the watched mistake residuals is steady with stochastic blunder. This procedure is straightforward with a bite the dust moving similarity. When you roll a pass on, you shouldn't have the capacity to foresee which number will appear on any given hurl. Not with standing, you can survey a progression of hurls to figure out if the showed numbers take after an arbitrary example. In the event that the number six appears more every now and again than irregularity directs, you know something isn't right with your comprehension of how incredible carries on. In the event that a card shark took a gander at the examination of kick the bucket moves, he could conform his mental model, and playing style, to figure the higher recurrence of sixes. His new mental model better mirrors the result. These remaining plots can be utilized to survey the nature of the relapse. You can look at the fundamental measurable suppositions about residuals, for example, steady fluctuation, freedom of variables and ordinariness of the dissemination. For these presumptions to remain constant for a specific relapse show, the residuals would need to be arbitrarily conveyed around zero.

Distinctive sorts of remaining plots can be utilized to check the legitimacy of these suppositions and give data on the most proficient method to enhance the model. For instance, the disperse plot of the residuals will be disarranged if the relapse is great. The residuals ought not demonstrate any pattern. A pattern would show that the residuals were not autonomous. Then again, a histogram plot of the residuals ought to display a symmetric ringer molded dissemination, demonstrating that the typicality presumption is prone to be valid.

SUMMARY OUTPUT Regression Statistics Multiple R 0.2440772 R Square 0.059573679 Adjusted R Square 0.044879518 Standard Error 0.020239941 Observations 131 ANOVA df SS MS F Significance F Regression 2 0.003321682 0.001660841 4.05424157 0.019623914 Residual 128 0.052435865 0.000409655 Total 130 0.055757547 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -0.001584388 0.015881845 -0.099760928 0.920690205 -0.033009331 0.029840555 -0.033009331 0.029840555 Cost of Living 0.000385361 0.000160911 2.394867311 0.01807552 6.69706E-05 0.000703751 6.69706E-05 0.000703751 Population -3.40861E-10 7.82243E-10 -0.435747736 0.663753732 -1.88866E-09 1.20694E-09 -1.88866E-09 1.20694E-09

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