Question

Step 4:

What percent of the variation in corn yield is explained by these two variables? Give your answers to 2 decimal places and do not include units in your answers.

Percent explained by the model = %

Step 5:

Using the regression equation, find a point estimate for the corn yield for 2014 Assume that the soy bean yield for that year is 42.

Point Estimate = (Give your answer to 1 decimal place.)

ID      Year    CornYield       SoyBeanYield
1       1957    48.3    23.2
2       1958    52.8    24.2
3       1959    53.1    23.5
4       1960    54.7    23.5
5       1961    62.4    25.1
6       1962    64.7    24.2
7       1963    67.9    24.4
8       1964    62.9    22.8
9       1965    74.1    24.5
10      1966    73.1    25.4
11      1967    80.1    24.5
12      1968    79.5    26.7
13      1969    85.9    27.4
14      1970    72.4    26.7
15      1971    88.1    27.5
16      1972    97      27.8
17      1973    91.3    27.8
18      1974    71.9    23.7
19      1975    86.4    28.9
20      1976    88      26.1
21      1977    90.8    30.6
22      1978    101     29.4
23      1979    109.5   32.1
24      1980    91      26.5
25      1981    108.9   30.1
26      1982    113.2   31.5
27      1983    81.1    26.2
28      1984    106.7   28.1
29      1985    118     34.1
30      1986    119.4   33.3
31      1987    119.8   33.9
32      1988    84.6    27.0
33      1989    116.3   32.3
34      1990    118.5   34.1
35      1991    108.6   34.2
36      1992    131.5   37.6
37      1993    100.7   32.6
38      1994    138.6   41.4
39      1995    113.5   35.3
40      1996    127.1   37.6
41      1997    126.7   38.9
42      1998    134.4   38.9
43      1999    133.8   36.6
44      2000    136.9   38.1
45      2001    138.2   39.6
46      2002    129.3   38.0
47      2003    142.2   33.9
48      2004    160.3   42.2
49      2005    147.9   43.1
50      2006    149.1   42.9
51      2007    150.7   41.7
52      2008    153.9   39.7
53      2009    164.7   44.0
54      2010    152.8   43.5
55      2011    147.2   41.9
56      2012    123.4   39.8
57      2013    158.8   43.3

Answer 1

Step 4:

The coefficient of determination R square = 94.80%

There is 94.795 percentage of variation in corn yield which is explained by all independent variables in the model namely year, year square, soybean yield.

Step 5:

regression equation: corn yield = -20.927 + 1.401*year -0.013*year^2 + 3.1646*SoyBeanYield

when,
year = 58.0000
year^2 = 3364.0000
SoyBeanYield = 42
preicted corn yield = -20.9272+1.4014*58-0.0134*3364+3.1647*42 = 148.2

data:

ID	Year	CornYield		year	year^2	SoyBeanYield
1	1957	48.3		1	1	23.2
2	1958	52.8		2	4	24.2
3	1959	53.1		3	9	23.5
4	1960	54.7		4	16	23.5
5	1961	62.4		5	25	25.1
6	1962	64.7		6	36	24.2
7	1963	67.9		7	49	24.4
8	1964	62.9		8	64	22.8
9	1965	74.1		9	81	24.5
10	1966	73.1		10	100	25.4
11	1967	80.1		11	121	24.5
12	1968	79.5		12	144	26.7
13	1969	85.9		13	169	27.4
14	1970	72.4		14	196	26.7
15	1971	88.1		15	225	27.5
16	1972	97		16	256	27.8
17	1973	91.3		17	289	27.8
18	1974	71.9		18	324	23.7
19	1975	86.4		19	361	28.9
20	1976	88		20	400	26.1
21	1977	90.8		21	441	30.6
22	1978	101		22	484	29.4
23	1979	109.5		23	529	32.1
24	1980	91		24	576	26.5
25	1981	108.9		25	625	30.1
26	1982	113.2		26	676	31.5
27	1983	81.1		27	729	26.2
28	1984	106.7		28	784	28.1
29	1985	118		29	841	34.1
30	1986	119.4		30	900	33.3
31	1987	119.8		31	961	33.9
32	1988	84.6		32	1024	27
33	1989	116.3		33	1089	32.3
34	1990	118.5		34	1156	34.1
35	1991	108.6		35	1225	34.2
36	1992	131.5		36	1296	37.6
37	1993	100.7		37	1369	32.6
38	1994	138.6		38	1444	41.4
39	1995	113.5		39	1521	35.3
40	1996	127.1		40	1600	37.6
41	1997	126.7		41	1681	38.9
42	1998	134.4		42	1764	38.9
43	1999	133.8		43	1849	36.6
44	2000	136.9		44	1936	38.1
45	2001	138.2		45	2025	39.6
46	2002	129.3		46	2116	38
47	2003	142.2		47	2209	33.9
48	2004	160.3		48	2304	42.2
49	2005	147.9		49	2401	43.1
50	2006	149.1		50	2500	42.9
51	2007	150.7		51	2601	41.7
52	2008	153.9		52	2704	39.7
53	2009	164.7		53	2809	44
54	2010	152.8		54	2916	43.5
55	2011	147.2		55	3025	41.9
56	2012	123.4		56	3136	39.8
57	2013	158.8		57	3249	43.3