Question

In: Statistics and Probability

For the data below, write an appropriate two-tailed, nondirectional null and alternative hypothesis, calculate the df,...

For the data below, write an appropriate two-tailed, nondirectional null and alternative hypothesis, calculate the df, and find the critical value. (up to 10 points)

X Y

Years of Education Number of Arrests

12 5

9 9

17 0

15 0

13 2

10 6

What is the coefficient of determination? Describe how to calculate the coefficient of determination. What information does this give us? (up to 5 points)

A professor calculated a correlation coefficient of 0.65 in a recent analysis. Based on this value, calculate the percentage of variance in the dependent variable is attributable to the independent variable? Don’t forget to interpret your results. (up to 5 points)

Expert Solution

1)

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	76	22	45.33333333	65.3	-51.67
mean	12.67	3.67	SSxx	SSyy	SSxy

sample size ,   n =   6
here, x̅ = Σx / n=   12.67   ,     ȳ = Σy/n =   3.67

SSxx =    Σ(x-x̅)² =    45.3333
SSxy=   Σ(x-x̅)(y-ȳ) =   -51.7

estimated slope , ß1 = SSxy/SSxx =   -51.7   /   45.333   =   -1.1397

intercept,   ß0 = y̅-ß1* x̄ =   18.1029

so, regression line is   Ŷ =   18.1029   +   -1.1397   *x

SSE=   (SSxx * SSyy - SS²xy)/SSxx =    6.449

std error ,Se =    √(SSE/(n-2)) =    1.270

correlation coefficient ,    r = Sxy/√(Sx.Sy) =   -0.9494

1)coefficient of determination = R² =    (Sxy)²/(Sx.Sy) =    0.9013

2)It means 90.13 % of variatiion in Y(Number of Arrests) can be explained by X(Years of Education)

3)

R = 0.65

R square = 0.4225

t means 42.25% of variatiion in Y(Number of Arrests) can be explained by X(Years of Education)

-----------------------------------------------------------

Ho:   ρ = 0       tail=   2
Ha:   ρ ╪ 0
n=   6
alpha,α =    0.01
correlation , r=   -0.9494
t-test statistic = r*√(n-2)/√(1-r²) =        -6.044
DF=n-2 =   4

critical t-value =    4.6041

Please revert in case of any doubt.

Please upvote. Thanks in advance

orchestra answered 1 year ago

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