Question

Researchers in China are looking at different varieties of peanuts. See table below to see phenotypic data for 2 different varieties of peanut (Xuhua and Fuchuan) and the offspring of their cross (F2). Each value represents a mean of a population for that variety. So, line 1 is 1 population for each of the parent varieties and their F2.

3. Are seed length and seed width correlated with each other (this has to be looked at within population)?

a. Calculate the correlation. Are they correlated?

b. Why do you think they are or are not correlated – think would you expect them to be and does what you find match or not match your expectation?

Line	Seed length			Seed width
	Xuhua	Fuchuan	F2	Xuhua	Fuchuan	F2
1	1.525	0.82	1.26	0.71	0.69	0.7
2	1.77	0.845	1.29	0.7	0.68	0.68
3	1.615	0.88	1.32	0.68	0.70	0.71
4	1.58	0.91	1.23	0.72	0.66	0.68
5	1.985	0.825	1.37	0.7	0.67	0.71
6	1.44	0.94	1.15	0.74	0.67	0.67
7	1.505	0.995	1.31	0.72	0.68	0.72
8	1.405	0.975	1.2	0.75	0.7	0.72
9	1.39	1.05	1.24	0.67	0.68	0.69

Answer 1

Correlations are the relationships between two variables, such as seed length and seed width. Positive correlations occur when both variables increase together, while negative correlations apply when an increase in one is associated with a decrease in the other or vice versa The given data is as follows: Seed length Seed width Line Xuhu Fuchua | F2 1.3 0.71 1.3 0.7 1.3 0.68 Xuhua Fuchuan F2 1 1.525 0.82 0.69 0.7 2 1.77 0.845 0.68 0.7 0.88 3 1.615 0.7 0.7 1.2 0.72 0.66 4 1.58 0.91 0.7 0.825 1.4 0.7 0.67 0.7 1.985 0.67 0.7 1.2 0.74 1.3 0.72 6 1.44 0.94 7 1.505 0.995 0.68 0.7 1.2 0.75 1.2 0.67 0.7 0.975 1.405 0.7 1.39 0.7 1.05 0.68 (a) Formula to calculate the Correlation is as follows n(Σxy) - (Σx)(Σ) νinΣ-(Ση Σy- (Σyl r- For example, if population 1 is considered to calculate the correlation, between seed length and seed width of Xuhua, then C

n(Σx) - (Σx) (Σ) V[nΣ-(ΣxΤηΣy-(Σy)1 9(1.08275)-(1.525) (0.71) x 2.3 26- (2.326)219x 0.5041- (0.5041)] r(1Xuhua) 1.00 For example, if population 1 is considered to calculate the correlation, between seed length and seed width of Fuchuan, then n(Σxy)- (Σx)(Σν) ηΣ-Σ) ΤηΣy-(Συ 9(0.5658)-(0.82)(0.69) 90x6 0.672-(0.672) ][9 x0.4761- (0.4761)] rlFuchuan) 0.95 For example, if population 1 is considered to calculate the correlation, between seed length and seed width of F2, then n(Σ3y )-(Σx) (Σν) r(F) -nΣ- (ΣIn Σν' - (Σν)*] 9(0.882)-(1.3)(0.7) 9x1.588- (1.588)2[9x0.4761- (0.4761)] -1.00 Since, for the population 1 the correlation values between seed length and seed width of Xuhua, Fuchuan and F2 have the value almost equal to 1.00. So, it has a tight clustering and it has a perfect positive correlation. (b) They are correlated because whenever there is an increase in the length of the seed there is an increase in the width of the seed