Question

It's commonly believed that throwing rice at weddings causes birds to explode. Here are data from four weddings: Pounds of Number of thrown rice exploding birds (y) Uw una The next bunch of questions will require you to perform the bivariate regression, compute the standard error for the coefficient, compute R2 and perform an F test, so keep track of your work as you go along Let's hit a least square regression equation y=a+bx with this data, What is the estimated coefficient b? POPOLE? 9WPNO MacBook Pro

Answer 1

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
3	4	6.25	5.06	5.63
5	6	0.25	0.06	0.13
7	7	2.25	0.56	1.13
7	8	2.25	3.06	2.63

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	22	25	11	8.750	9.500
mean	5.500	6.250	SSxx	SSyy	SSxy

sample size ,   n =   4          
here, x̅ = Σx / n=   5.50   ,     ȳ = Σy/n =   6.25  
                  
SSxx =    Σ(x-x̅)² =    11.0000          
SSxy=   Σ(x-x̅)(y-ȳ) =   9.5          
                  
estimated slope , ß1 = SSxy/SSxx =   9.5   /   11.000   =   0.86364
                  
intercept,   ß0 = y̅-ß1* x̄ =   1.50000          
                  
so, regression line is   Ŷ =   1.50 +   0.8636*x

estimated coefficient b = 0.8636

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estimated std error of slope =Se(ß1) = Se/√Sxx =    0.522   /√   11.00   =   0.1575

estimated std error of intercept =Se(ßo) =    Se*√(1/n+x̅²/Sxx)=       0.905

R² =    (Sxy)²/(Sx.Sy) =    0.9377

Anova table
variation	SS	df	MS	F-stat	p-value
regression	8.2045	1	8.2045	30.08	0.0317
error,	0.5455	2	0.2727
total	8.7500	3

F value = 30.08