Question

B. Calculate Pearson's r. C. Calculate the y-intercept, slope, and draw a the data in the table below to answer the six questions regression line on the scatterplot. D. Answer the “Prediction" problem. E. Calculate 12 and explain what it tells us about the relationship between the variables. Calculate the t-ratio for Pearson's r and deter- mine the level of significance. above. 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

B-F show work please

Answer 1

Solution-:

Given: X= Percent people of color and Y= Number of toxic waste sites

> X=c(6,20,14,3,9,22,11,8,31,16);X
[1] 6 20 14 3 9 22 11 8 31 16
> Y=c(3,14,10,4,8,17,6,3,15,10);Y
[1] 3 14 10 4 8 17 6 3 15 10
> #(B) Correlation
> r=cor(X,Y);r
[1] 0.9013878
> round(r,2)
[1] 0.9
> #(C)For regression equation
> fit=lm(Y~X);fit

Call:
lm(formula = Y ~ X)

Coefficients:
(Intercept) X
1.4167 0.5417

> #The equation of the line of regression of Y on X is: Y= m*X+b or y=a+b*X
> #The equation of the line of regression of Y on X is:Y=1.4167+0.5417*X   
> # For Scatter diagram
> plot(X,Y,xlab=" % People of color",ylab="Number of toxic waste sites",main="Scatter Diagram X Vs Y ")

Scatter Diagram X Vs Y 16 14 o 12 Number of toxic waste sites 10 - 9 4 O o 5 10 15 20 25 30 % People of color

> #Comment: This scatter diagram shows highly positive correlation.
> #(D)The goal of a prediction problem is to give the correct label (e.g. prediction or. output) to an instance
> #If you have a model that adequately fits the data, use it to make predictions.
> #(E)coefficient of determination
> rr=r^2;rr
[1] 0.8125
> round(rr,2)
[1] 0.81
> #This indicate that there is relation between X and Y.

R-Code:

X=c(6,20,14,3,9,22,11,8,31,16);X
Y=c(3,14,10,4,8,17,6,3,15,10);Y
#(B) Correlation
r=cor(X,Y);r
round(r,2)
#(C)For regression equation
fit=lm(Y~X);fit  
#The equation of the line of regression of Y on X is: Y= m*X+b or y=a+b*X
#The equation of the line of regression of Y on X is:Y=1.4167+0.5417*X   
# For Scatter diagram
plot(X,Y,xlab=" % People of color",ylab="Number of toxic waste sites",main="Scatter Diagram X Vs Y ")
#Comment: This scatter diagram shows highly positive correlation.
#(D)The goal of a prediction problem is to give the correct label (e.g. prediction or. output) to an instance
#If you have a model that adequately fits the data, use it to make predictions.
#(E)coefficient of determination
rr=r^2;rr
round(rr,2)
#This indicate that there is relation between X and Y.