Model-Building and Diagnostics

A study obtained mortgage yields in n=18 U.S. metropolitan areas in the 1960s. The researcher obtained the following variables and fit a linear regression model to see which factors (variables) were associated with yield (each variable was obtained for each metro area):

• Y = Mortgage Yield (Interest Rate as a %)
• X₁ = Average Loan/Mortgage Ratio (High Values Low Down Payments/Higher Risk)
• X₂ = Distance from Boston (in miles) - (Most of population was in Northeast in the 1960s)
• X₃ = Savings per unit built (Measure of Available capital versus building rate)
• X₄ = Savings per capita
• X₅ = Population increase from 1950 to 1960 (%)
• X₆ = Percent of first mortgage from inter-regional banks (Measures flow of money from outside SMSA)

p.2.a. Using stepwise regression, based on AIC, choose the best model

p.2.b. Using all possible regressions, choose the best model, based on the C_p criterion

p.3.c. Obtain Studentized deleted residuals, hat values, DFFITS, Cooks D, and DFBETAS for each city, based on the model you selected in part a). any cities stand out as outliers or influential cases? Specifically give your "critical" cut-off value for each measure

NEED

Model-Building and Diagnostics

p.2.a. Model selected by Stepwise Regression:

p.2.b. Model Selected based on C_p from all possible regressions:

p.2.c. Cut-off values: (either from book/slides or using R's criteria):

Studentized Residuals: hat-values: DFFITS:

Cook's D: DFBETAS:

Influential Cases (if any):

smsa	mortYld	X1	X2	X3	X4	X5	X6
Los Angeles-Long Bea	6.17	78.1	3042	91.3	1738.1	45.5	33.1
Denver	6.06	77	1997	84.1	1110.4	51.8	21.9
San Francisco-Oaklan	6.04	75.7	3162	129.3	1738.1	24	46
Dallas-Fort Worth	6.04	77.4	1821	41.2	778.4	45.7	51.3
Miami	6.02	77.4	1542	119.1	1136.7	88.9	18.7
Atlanta	6.02	73.6	1074	32.3	582.9	39.9	26.6
Houston	5.99	76.3	1856	45.2	778.4	54.1	35.7
Seattle	5.91	72.5	3024	109.7	1186	31.1	17
New York	5.89	77.3	216	364.3	2582.4	11.9	7.3
Memphis	5.87	77.4	1350	111	613.6	27.4	11.3
New Orleans	5.85	72.4	1544	81	636.1	27.3	8.1
Cleveland	5.75	67	631	202.7	1346	24.6	10
Chicago	5.73	68.9	972	290.1	1626.8	20.1	9.4
Detroit	5.66	70.7	699	223.4	1049.6	24.7	31.7
Minneapolis-St Paul	5.66	69.8	1377	138.4	1289.3	28.8	19.7
Baltimore	5.63	72.9	399	125.4	836.3	22.9	8.6
Philadelphia	5.57	68.7	304	259.5	1315.3	18.3	18.7
Boston	5.28	67.8	0	428.2	2081	7.5	2