Question

The table below represents the number of young people in a certain city enrolled in the academic support and enrichment program of youth services. Here, x represents the number of months from January 2011, and y represents the number of young people enrolled. Use Excel to find the best fit linear regression equation. Round the slope and intercept to two decimal places.

x   y
0   3199
1   3282
2   3432
3   3245
4   3076
5   3485
6   1524
7   1880
8   2715
9   2963
10   2917
11   3064
12   2730
13   3002
14   3115
15   3148
16   3372
17   3070
18   1813
19   1820
20   2720
21   3297
22   3157
23   2932
24   2839
25   2738
26   2721
27   2999
28   807
29   221
30   1537
31   1922
32   2532
33   3070
34   3091
35   2965
36   2956
37   3116
38   3294
39   3271
40   3211
41   3383
42   2243
43   2035
44   2625
45   2970
46   3046
47   2785
48   2650
49   1121
50   204
51   2796
52   2692
53   2830
54   2068
55   1802
56   2181
57   2675
58   2625
59   2632
60   2354
61   2501
62   2476
63   2458
64   2391
65   2375

Answer 1

Months	Young People enrolled
0	3199
1	3282
2	3432
3	3245
4	3076
5	3485
6	1524
7	1880
8	2715
9	2963
10	2917
11	3064
12	2730
13	3002
14	3115
15	3148
16	3372
17	3070
18	1813
19	1820
20	2720
21	3297
22	3157
23	2932
24	2839
25	2738
26	2721
27	2999
28	807
29	221
30	1537
31	1922
32	2532
33	3070
34	3091
35	2965
36	2956
37	3116
38	3294
39	3271
40	3211
41	3383
42	2243
43	2035
44	2625
45	2970
46	3046
47	2785
48	2650
49	1121
50	204
51	2796
52	2692
53	2830
54	2068
55	1802
56	2181
57	2675
58	2625
59	2632
60	2354
61	2501
62	2476
63	2458
64	2391
65	2375

Upon regressing it in excel, we find the following results.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.261187
R Square	0.068219
Adjusted R Square	0.053659
Standard Error	688.5021
Observations	66
ANOVA
	df	SS	MS	F	Significance F
Regression	1	2221154	2221154	4.685631	0.034152
Residual	64	30338252	474035.2
Total	65	32559406
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	2921.54	167.59	17.43	0.00	2586.74	3256.34	2586.74	3256.34
Months	-9.63	4.45	-2.16	0.03	-18.52	-0.74	-18.52	-0.74

Therefore, the equation of the regression line is ,

Y( Number of People enrolled) = 2921.54 + -9.63* X (No of months from Jan 11)

Hope I answered the query.