Question

In: Statistics and Probability

5. You are given the following table. X Y 1,000 500 3,000 400 7,000 750 12,000...

5. You are given the following table.

X	Y
1,000	500
3,000	400
7,000	750
12,000	1,000
15,500	1,200
17,000	1,000
17,500	1,800
21,000	2000
22,800	2,200
23,000	3,000

a. Decide which variable should be the independent variable and which should be the dependent variable.

b. Draw a scatter plot of the data.

c. Does it appear from inspection that there is a relationship between the variables? Why or why not?

d. Calculate the least-squares line. Put the equation in the form of: ŷ = a + bx.

e. Find the correlation coefficient. Is it significant?

f. Find estimated total values for column Y for 16,000, 24,000, and 36,000 16,000= 24,000= 36,000=

g. Does it appear that a line is the best way to fit the data? Why or why not? h. Are there any outliers in the data?

i. Based on these results, what would be the probate fees and taxes for an estate that does not have any assets?

j. What is the slope of the least-squares (best-fit) line? Interpret the slope.

Expert Solution

5)

X: independent

Y : dependent

................

b)

c)

there appear to be linear , positive relation between x and y

...........

d)

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	139800	13850	573936000	6310250.0	53587000.00
mean	13980.00	1385.00	SSxx	SSyy	SSxy

sample size ,   n =   10
here, x̅ = Σx / n=   13980.00   ,     ȳ = Σy/n =   1385.00

SSxx =    Σ(x-x̅)² =    573936000.0000
SSxy=   Σ(x-x̅)(y-ȳ) =   53587000.0

estimated slope , ß1 = SSxy/SSxx =   53587000.0   /   573936000.000   =   0.0934

intercept,   ß0 = y̅-ß1* x̄ =   79.7216

so, regression line is   Ŷ =   79.7216   +   0.0934   *x

..........................

e)

correlation coefficient , r = Sxy/√(Sx.Sy) = 0.8904

correlation hypothesis test
Ho:   ρ = 0
Ha:   ρ ╪ 0
n=   10
alpha,α =    0.05
correlation , r=   0.8904
t-test statistic = r*√(n-2)/√(1-r²) =        5.534
DF=n-2 =   8
p-value =    0.0006
Decison:   p value < α , So, Reject Ho

................

f)

Predicted Y at X=   16000   is
Ŷ =   79.72161   +   0.093368   *   16000   =   1573.602
Predicted Y at X=   24000   is
Ŷ =   79.72161   +   0.093368   *   24000   =   2320.543

Predicted Y at X= 32000 is
Ŷ = 79.72161 + 0.093368 * 32000 = 3067.483
..............

thanks

please upvote

orchestra answered 2 years ago

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