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MAT 273 — Applied Statistics

PROJECT II

50 points

This project is to be done in groups of three people. You may submit only one final project for the group.

Passing Rate for the 12th Grade Proficiency Examination – c. 1995

This project is a regression study done on the rate at which students in schools in northwest Ohio passed the 12th grade proficiency examinations about the year 1995. (This is the year for which I have data.) The data comprises 8 variables for 88 districts. 6 additional school districts’ data has been placed at the right of the sheet. These have been removed from the data because they are outliers. A detailed description of the variables in the data set is below, and the data file is in the web portal. Your job is to do a regression analysis, and then think about the results and draw conclusions.

Use the “Project 2 Data Schools file to complete the following:

1. Using the data in the Welfare Percentage Data sheet, produce a scatter plot with the passing rate as the response variable and ‘Percent of Families Receiving Welfare in the District’ as the explanatory variable. Print as a full page.

2. Repeat Step 1. using ‘Instructional Spending per Student’ as the explanatory variable in the Instructional Spending Data sheet. Print as a full page.

3. Repeat Step 2. using the ‘Average Daily Attendance Rate’ as the explanatory variable in the Attendance Data sheet. Print as a full page.

4. Run a simple regression with the passing rate as the response variable and ‘Percent of Families Receiving Welfare in the District’ as the explanatory variable. On the results sheet :

Indicate the correlation coefficient (R)

Interpret the coefficient of determination (R²)

Interpret the significance

Give the linear regression equation

Use the regression equation to predict one passing rate value.

Note: These can be written by hand on the printouts, or typed into the sheet before printing. Print this as one page.

5. Run a simple regression with the passing rate as the response variable and ‘Instructional Spending per Student’ as the explanatory variable. On the Results sheet :

Indicate the correlation coefficient (R)

Interpret the coefficient of determination (R²)

Interpret the significance

Give the linear regression equation

Use the regression equation to predict one passing rate value.

Note: These can be written by hand on the printouts, or typed into the sheet before printing. Print this as one page.

6. Run a simple regression with the passing rate as the response variable and ‘Average Daily Attendance Rate’ as the explanatory variable. On the Results sheet :

Indicate the correlation coefficient (R)

Interpret the coefficient of determination (R²)

Interpret the significance

Give the linear regression equation

Use the regression equation to predict one passing rate value.

Note: These can be written by hand on the printouts, or typed into the sheet before printing. Print this as one page.

Report your findings:

Submit a typewritten 6-paragraph summary of the assignment and your findings. The summary should be formatted with one paragraph each for the introduction and conclusion and one paragraph of ANALYSIS/INTERPRETATION for each of the four questions below. Attach a copy of the EXCEL printouts to the report. Put the scatterplots first and the regression results second. Do not forget to write the interpretations on the regression printouts.

The questions you are asked to consider are:

· Are any of the three possible explanatory variables significantly tied to the passing rate? Which one or ones? Justify your answer using significance.

· Which of the three possible explanatory variables is the best predictor of the passing rate? Justify your answer using correlation.

· Do any of the relationships look nonlinear? Which one or ones?

· Are any of the regression equations surprising? Which one or ones?

Print your paper.

Attach a copy of the EXCEL printouts to the report. Put the scatterplots first and the regression results second. Do not forget to write the interpretations on the regression printouts!

Schools	Students	Income	Property	Welfare	Salary	Instruct	Attend	Passing
	X1	X2	X3	X4	X5	X6	X7	Y
Bluffton	1132	24487	62678	1.80	31221	2130	95.70	85
Shawnee	2472	29777	130910	2.60	34860	2570	94.70	73
Spencerville	1026	23161	51645	5.40	30155	2262	95.50	68
Delphos	1104	21792	88453	6.20	32273	2506	96.50	65
Elida	3204	24446	65550	8.90	32876	2250	94.10	62
Northeastern	1194	26428	88789	1.70	30919	2431	96.10	72
Ayersville	921	28228	82707	3.90	32850	2693	95.60	68
Defiance	3046	23812	56333	11.20	34750	2438	94.20	63
Hicksville	990	22448	56411	7.00	34224	2351	95.70	59
Central	1216	24189	53923	4.60	34430	2496	94.80	56
Berlin-Milan	1593	25223	76878	4.00	32166	2564	96.10	77
Perkins	2038	25586	117545	3.30	39352	2861	95.80	74
Huron	1494	27135	105588	4.60	33433	2968	95.40	74
Margaretta	1560	23849	74601	2.80	37084	2464	95.50	66
Sandusky	4426	19529	72425	25.20	36042	2766	93.00	37
Pettisville	503	25079	53948	3.90	31159	2834	96.10	78
Wauseon	1864	23408	60896	4.90	32499	2252	95.30	75
Evergreen	1238	23826	69432	5.20	32353	2250	95.00	72
Archbold-Area	1401	26706	107547	4.10	35982	2837	96.20	69
Pike-Delta-York	1559	23396	48638	6.10	31310	2309	94.80	66
Gorham-Fayette	487	22405	57221	6.90	33166	2492	94.60	51
Swanton	1725	24596	69320	6.30	33690	2615	94.90	50
Arlington	685	26175	55478	2.70	31821	2205	96.50	84
Vanlue	346	24709	49606	4.10	28411	2420	96.20	83
Liberty-Benton	954	28718	77503	1.50	30330	2063	96.70	78
Van Buren	840	28964	151992	1.80	33447	2584	96.40	75
Cory-Rawson	794	23904	69242	2.40	31241	2416	96.40	73
Arcadia	597	24305	78102	2.50	30738	2752	95.90	64
McComb	805	23754	69347	5.70	28986	2321	95.90	61
Findlay	5758	24269	92648	7.60	35879	2860	94.90	60
Ada	855	23029	52655	5.30	28479	2380	95.90	69
Kenton	2228	20418	61155	13.80	30907	2512	93.70	54
Liberty Center	1009	24723	57685	4.10	30904	2431	95.80	82
Patrick Henry	1176	23061	63134	5.20	31895	2552	95.90	75
Napoleon Area	2331	25304	84245	6.60	32773	2422	94.60	73
Holgate	605	23962	49709	6.00	31324	2454	94.90	71
Monroeville	686	22942	63103	4.30	30838	2474	95.80	64
Bellevue	2276	24025	66912	6.90	32164	2374	95.10	55
Willard	2300	23304	58832	14.30	35042	2347	94.60	53
Norwalk	2650	21551	72266	12.20	37145	2384	94.00	50
Anthony Wayne	3178	29215	88004	3.10	35617	2844	95.30	75
Sylvania	7822	32114	101503	3.80	39684	2943	95.50	72
Maumee	3009	27604	117921	3.90	41634	3933	95.00	69
Oregon	3594	24525	123599	8.70	35848	2941	94.70	52
Washington	7154	23507	102485	11.80	39155	2997	93.70	51
Springfield	3575	26048	98346	12.20	34437	2774	93.80	49
Benton Carroll Salem	2063	23899	237206	4.70	42734	3444	95.60	81
Danbury	635	21325	182360	3.20	34971	3158	95.30	65
Genoa	1584	25321	53120	4.80	34661	2845	95.90	65
Port Clinton	2238	20941	129961	10.50	39542	2926	94.50	50
Paulding	1993	22677	46163	8.60	32928	2560	94.50	59
Columbus Grove	866	23562	55568	8.40	30476	2174	96.20	84

Schools	Students	Income	Property	Welfare	Salary	Instruct	Attend	Passing
Kalida	775	24456	44267	0.70	28962	2274	96.80	81
Continental	792	23625	37277	10.00	28945	2225	95.50	79
Ottawa-glandorf	1749	25363	64288	6.50	31185	2154	96.50	77
Pandora-Gilboa	632	23806	55446	1.20	27693	2078	96.50	67
Leipsic	748	20941	62648	16.10	30282	2811	93.90	47
Gibsonburg	983	23312	46098	17.80	31244	2242	94.40	71
Lakota	1332	22678	55933	10.50	30765	2306	95.20	66
Fremont	5156	22327	74874	16.20	37759	2616	94.70	57
Woodmore	1141	26460	90484	10.90	32296	2227	96.50	56
Clyde-Green Springs	2368	23854	55724	7.00	33998	2383	94.60	47
Bettsville	347	22103	37269	6.10	27466	2394	95.80	83
Seneca East	1183	22656	50895	4.80	29940	2435	95.90	80
Old Fort	540	23208	50712	19.30	28195	2743	96.00	78
Hopewell-Loudon	870	22103	72201	4.70	30644	2564	94.60	74
New Riegel	459	23314	41376	2.70	29099	2501	97.00	73
Tiffin	3632	21246	65291	9.00	35513	2506	94.70	67
Fostoria	2742	20809	62268	20.40	34241	2455	92.70	34
Van Wert	2504	22728	67932	7.10	33885	2511	95.30	61
Edon-Northwest	744	23035	38462	2.70	30833	1916	95.10	73
Milcreek-West Unity	788	21302	40239	3.20	31582	2382	95.90	71
Bryan	2266	22607	81152	4.20	32643	2706	95.20	69
North Central	757	21871	59396	2.90	31978	2349	95.60	68
Montpelier	1172	20787	44383	8.20	33243	2654	94.80	67
Edgerton	767	22429	54040	4.10	28975	2470	95.90	61
Stryker	579	24084	65532	3.40	33855	2617	95.70	47
Perrysburg	3839	32773	97888	2.60	40320	3011	96.10	98
Elmwood	1237	22179	47644	7.50	30434	2643	95.20	68
Bowling Green	3534	21307	84682	7.50	37983	2849	94.70	68
Otsego	1643	24614	57601	5.00	36065	2539	95.40	64
Northwood	1091	25905	77077	7.90	35536	2979	94.90	61
Eastwood	1739	25043	67929	4.70	35742	2499	95.90	60
Lake	1665	23559	95859	6.20	38046	2820	95.20	55
Rossford	2087	25360	123725	7.20	39476	3258	94.90	54
North Baltimore	839	22075	58383	10.60	29579	2331	94.50	50
Upper Sandusky	1801	21063	68348	3.90	32778	2267	95.60	62
Carey	915	21658	51497	6.00	30968	2513	95.50	59

Removed from data:
Toledo	36790	21079	62668	42.80	36190	2611	90.70	28
	Outlier-Students, Welfare, Attendance
Ottawa Hills	933	45723	122356	0.20	43256	4150	95.70	95
	Outlier-Income
Kelleys Island	20	19854	802081	11.40	27144	11226	95.00	100
	Outlier-Property, Instruct
Put-in-Bay	70	19266	426419	1.40	30242	7824	94.50	33
	Outlier-Property, Instruct
Lima	5963	18394	44138	33.80	33142	2657	92.30	40
	Outlier-Welfare
Ottoville	610	24128	46582	0.20	26125	2588	99.80	86
	Outlier-Attendance

Variable Name	Description
Students	Number of students in the school district.
Income	Mean family income in the district.
Property	Mean property value in the district
Welfare	Percent of families receiving welfare.
Salary	Mean salary of classroom teachers.
Instruct	Amount spent per pupil.
Attend	Mean daily attendance rate
Passing	Percent passing the 12th grade proficiency examination.