Question

For the Florida data file (below) giving countywide data in Florida for several variables, a moderate positive correlation (r = 0.47) exists between crime rate and percent who are high school graduates. The percentage living in urban areas is also strongly correlated with crime rate (r = 0.68) and with high school graduation rate (r = 0.79).

a. Explain why the association between crime rate and high school graduation rate could disappear, or even change direction, when we control for percentage living in urban areas.

b. Under the control in (a), if the association disappears, which type of relationship is more plausible-- a spurious relationship or a chain relationship?  

County	Crime	Income	HS	Urban
ALACHUA	104	22.1	82.7	73.2
BAKER	20	25.8	64.1	21.5
BAY	64	24.7	74.7	85
BRADFORD	50	24.6	65	23.2
BREVARD	64	30.5	82.3	91.9
BROWARD	94	30.6	76.8	98.9
CALHOUN	8	18.6	55.9	0
CHARLOTTE	35	25.7	75.7	80.2
CITRUS	27	21.3	68.6	31
CLAY	41	34.9	81.2	65.8
COLLIER	55	34	79	77.6
COLUMBIA	69	22	69	31.1
DADE	128	26.9	65	98.8
DESOTO	69	21	54.5	44.6
DIXIE	49	15.4	57.7	0
DUVAL	97	28.5	76.9	98.8
ESCAMBIA	70	25.2	76.2	85.9
FLAGLER	34	28.6	78.7	63.1
FRANKLIN	37	17.2	59.5	30.2
GADSDEN	52	20	59.9	28.8
GILCHRIST	15	20.6	63	0
GLADES	62	20.7	57.4	0
GULF	19	21.9	66.4	35.2
HAMILTON	6	18.7	58.4	0
HARDEE	57	22.1	54.8	16.7
HENDRY	47	24.9	56.6	44.7
HERNANDO	44	22.7	70.5	61.3
HIGHLANDS	56	21.1	68.2	24.8
HILLSBOROUGH	110	28.5	75.6	89.2
HOLMES	5	17.2	57.1	16.8
INDIAN_RIVER	58	29	76.5	83
JACKSON	32	19.5	61.6	21.7
JEFFERSON	36	21.8	64.1	22.3
LAFAYETTE	0	20.7	58.2	0
LAKE	42	23.4	70.6	43.2
LEE	59	28.4	76.9	86.1
LEON	107	27.3	84.9	82.5
LEVY	45	18.8	62.8	0
LIBERTY	8	22.3	56.7	0
MADISON	26	18.2	56.5	20.3
MANATEE	79	26	75.6	88.7
MARION	64	22.5	69.6	39.6
MARTIN	53	31.8	79.7	83.2
MONROE	89	29.4	79.7	73.2
NASSAU	42	30.2	71.2	44.9
OKALOOSA	37	27.9	83.8	84
OKEECHOBEE	51	21.4	59.1	30.1
ORANGE	93	30.3	78.8	93.1
OSCEOLA	78	27.3	73.7	66.4
PALM_BEACH	90	32.5	78.8	94.7
PASCO	42	21.5	66.9	67.4
PINELLAS	70	26.3	78.1	99.6
POLK	84	25.2	68	70.3
PUTNAM	83	20.2	64.3	15.7
SANTA_R	43	27.6	79.9	57.2
SARASOTA	58	29.9	71.7	92.1
SEMINOLE	56	35.6	78.5	44.4
ST_JOHNS	54	29.9	81.3	93.2
ST_LUCIE	58	27.7	84.6	92.8
SUMTER	37	19.6	64.3	19.3
SUWANEE	37	19.8	63.8	23.6
TAYLOR	76	21.4	62.1	41.8
UNION	6	22.8	67.7	0
VOLUSIA	62	24.8	75.4	83.9
WAKULLA	29	25	71.6	0
WALTON	18	21.9	66.5	20.9
WASHINGTON	21	18.3	60.9	22.9

Answer 1