Question

C. Calculate the y-intercept, slope, and draw a Exercises For each of the problems below: A. Draw a scatterplot. B. Calculate Pearson's regression line on the scatterplot. D. Answer the "Prediction" problem. E. Calculate r and explain what it tells us about the relationship between the variables. F. Calculate the t-ratio for Pearson's r and deter- mine the level of significance. 1. Sociologists have discovered a phenomenon known as "environmental racism," a condition that exists when people of color bear a disproportionate burden of en- vironmental hazards relative to whites. Suppose we sample 10 communities to determine the number of toxic waste sites in each community and the percent of each community's population that is nonwhite. Use the data in the table below to answer the six questions above. PERCENT PEOPLE OF COLOR (X) NUMBER OF TOXIC WASTE SITES (Y 6 3 20 14 10 14 4 3 8 9 22 17

B-F

Answer 1

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	74.00	56.00	293.33	151.3	205.33
mean	12.33	9.33	SSxx	SSyy	SSxy

b) correlation coefficient ,    r = SSxy/√(SSx.SSy) =   0.9746

c)

Sample size,   n =   6
here, x̅ = Σx / n=   12.333  
ȳ = Σy/n =   9.333  
SSxx =    Σ(x-x̅)² =    293.3333
SSxy=   Σ(x-x̅)(y-ȳ) =   205.3
      
estimated slope , ß1 = SSxy/SSxx =   205.3333/293.3333=   0.7000
intercept,ß0 = y̅-ß1* x̄ =   9.3333- (0.7 )*12.3333=   0.7000

Scatterplot 18 16 14 12 10 8 6 4 2 0 0 5 10 15 20 25 х

d)

Regression line is, Ŷ=   0.700   + (   0.700   )*x

e)

R² =    (SSxy)²/(SSx.SSy) =    0.950
Approximately    94.98%   of variation in observations of variable Y, is explained by variable x

f)

Ho:   ρ = 0  
Ha:   ρ ╪ 0  
n=   6  
alpha,α =    0.05  
correlation , r=   0.9746  
t-test statistic = r*√(n-2)/√(1-r²) =        8.6977
DF=n-2 =   4  
p-value =    0.0010  
Decison:   p value < α , So, Reject Ho  

There is enough evidence of significant correlation