Question

Virginia bluebells have flowers that can be blue or white. The data below contains data on pollination rates for plants (numpoll) with either blue or white flowers (color), and the number of flowers on each plant (plsize). Do the regressions of number of flowers pollinated on plant size (number of flowers) for blue and white flowers have the same slopes and intercepts? Are the regressions coincident or parallel? PLS USE R SYNTAX/R MARKDOWN

color	plsize	numpoll	colorcode
white	6	2	0
white	12	9	0
white	22	11	0
white	14	11	0
white	16	9	0
white	13	10	0
white	11	8	0
white	8	4	0
white	4	1	0
white	24	14	0
white	5	4	0
white	15	11	0
blue	24	19	1
blue	4	4	1
blue	9	5	1
blue	14	12	1
blue	17	13	1
blue	12	10	1
blue	10	7	1
blue	6	5	1
blue	18	15	1

Answer 1

R codes:

> w_plsize=scan('clipboard');w_plsize
Read 12 items
[1] 6 12 22 14 16 13 11 8 4 24 5 15
> w_numpoll=scan('clipboard');w_numpoll
Read 12 items
[1] 2 9 11 11 9 10 8 4 1 14 4 11
> b_plsize=scan('clipboard');b_plsize
Read 9 items
[1] 24 4 9 14 17 12 10 6 18
> b_numpoll=scan('clipboard');b_numpoll
Read 9 items
[1] 19 4 5 12 13 10 7 5 15
> model1=lm(w_numpoll~w_plsize)
> summary(model1)

Call:
lm(formula = w_numpoll ~ w_plsize)

Residuals:
Min 1Q Median 3Q Max
-2.48551 -1.31102 -0.02326 1.51793 2.27422

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.39626 1.16862 0.339 0.742
w_plsize 0.59497 0.08419 7.067 3.43e-05 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.76 on 10 degrees of freedom
Multiple R-squared: 0.8332, Adjusted R-squared: 0.8165
F-statistic: 49.94 on 1 and 10 DF, p-value: 3.429e-05

> model2=lm(b_numpoll~b_plsize)
> summary(model2)

Call:
lm(formula = b_numpoll ~ b_plsize)

Residuals:
Min 1Q Median 3Q Max
-2.0482 -0.4885 0.3669 0.7065 0.9769

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.19706 0.83418 -0.236 0.82
b_plsize 0.80503 0.05962 13.503 2.87e-06 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.063 on 7 degrees of freedom
Multiple R-squared: 0.963, Adjusted R-squared: 0.9577
F-statistic: 182.3 on 1 and 7 DF, p-value: 2.87e-06

> plsize=c(w_plsize,b_plsize)
> numpoll=c(w_numpoll,b_numpoll)
> plot(plsize,numpoll)
> abline(model1)
> abline(model2)

15 numpoll 10 ooooo O 5 B 10 15 20 plsize

Slope and intercept of the two models namely for white and blue flowers are different.

Regression line do not coincide with each other.