Statistics question

Anonymous
timer Asked: Jul 2nd, 2018
account_balance_wallet $15

Question description

Attached below is 20 questions for my elementary to statistics please help any way you can as this stuff doesn’t make sense to me. thank you!

Statistics question
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Statistics question
9d829cb7_8d60_4ff2_b4bc_026c4c754141.jpeg

Tutor Answer

uoscar
School: Carnegie Mellon University

Please, use this attachment. I made some corrections to the solution of Q9 and Q10.Please give me feedback.

Q1: What is the predictor variable?
Answer: The predictor variable is number of Hours Studied.

Q2: What is the criterion variable?
Answer: The criterion variable is Score on Quiz.

Q3: What is the covariance?
Solution:
COV(X, Y) = SXY =
𝑋̅ =

βˆ‘ π‘₯ 11
=
= 2.75
𝑛
4

∴ SXY =

π‘ŒΜ… =

βˆ‘ (𝑋𝑖 βˆ’ 𝑋̅)(π‘Œπ‘– βˆ’ π‘ŒΜ…)
π‘›βˆ’1

βˆ‘ 𝑦 22
=
= 5.50
𝑛
4

(1 βˆ’ 2.75)(3 βˆ’ 5.50) + (2 βˆ’ 2.75)(5 βˆ’ 5.50) + (3 βˆ’ 2.75)(5 βˆ’ 5.50) + (5 βˆ’ 2.75)(9 βˆ’ 5.50)
nβˆ’1

SXY =

(βˆ’1.75)(βˆ’2.5) + (βˆ’0.75)(βˆ’0.5) + (0.25)(βˆ’0.5) + (2.25)(3.5)
4βˆ’1

SXY =

4.375 + 0.375 βˆ’ 0.125 + 7.875 12.5
=
= 4.1667
3
3

Answer: The covariance is 4.1667
Alternatively:
COV(X, Y) =

βˆ‘ π‘‹π‘Œ βˆ’ π‘ŒΜ… βˆ‘ 𝑋 βˆ’ 𝑋̅ βˆ‘ π‘Œ + π‘›π‘‹Μ…π‘ŒΜ… 73 βˆ’ (5.5)(11) βˆ’ 2.75(22) + 4(2.75)(5.5) 12.5
=
=
π‘›βˆ’1
4βˆ’1
3

Answer: The covariance is 4.1667

Q4: What is the standard deviation of the predictor variable?
Solution
The predictor variable is X (i.e. the number of hours studied). The standard deviation is given by:
Μ… βˆ‘ 𝑋 + 𝑛𝑋
Μ…2
βˆ‘ (𝑋𝑖 βˆ’ 𝑋̅)2
βˆ‘ 𝑋2 βˆ’ 2𝑋
√
𝑆𝑋 = √
=
π‘›βˆ’1
π‘›βˆ’1
39 βˆ’ 2(2.75)(11) + 4(2.752 )
8.75
∴ 𝑆𝑋 = √
=√
= 1.7078
4βˆ’1
3
Answer: The standard deviation of the predictor variable is 1.7078
Q5: What is the standard deviation of the criterion variable?
Solution
The criterion variable is Y (i.e. Score on Quiz). The standard deviation is given by:
βˆ‘ (π‘Œπ‘– βˆ’ π‘ŒΜ…)2
βˆ‘ π‘Œ2 βˆ’ 2π‘ŒΜ… βˆ‘ π‘Œ + π‘›π‘ŒΜ… 2
√
√
π‘†π‘Œ =
=
π‘›βˆ’1
π‘›βˆ’1
140 βˆ’ 2(5.50)(22) + 4(5.502 )
19
√
∴ π‘†π‘Œ =
= √ = 2.5166
4βˆ’1
3
Answer: The standard deviation of the criterion variable is 2.5166
Q6: What is the Pearson’s r value?
Solution
The Pearson’s correlation coefficient, r is given by:
π‘Ÿ=

𝑛 βˆ‘ π‘₯𝑦 βˆ’ βˆ‘ π‘₯ βˆ‘ 𝑦
√[𝑛 βˆ‘ π‘₯ 2 βˆ’ (βˆ‘ π‘₯)2 ][𝑛 βˆ‘ 𝑦 2 βˆ’ (βˆ‘ 𝑦)2 ]

Alternatively, r can be computed from the standard deviation as:
π‘Ÿ=
βˆ΄π‘Ÿ=

π‘†π‘‹π‘Œ
𝑆𝑋 βˆ™ π‘†π‘Œ

4.1667
= 0.9695
1.7078 Γ— 2.5166

Answer: The Pearson’s r value is 0.9695

Q7: What is the best interpretation of your Pearson’s correlation in Q6?
Answer:
(A) As β€˜hours studied’ goes up, there is a corresponding increase in β€˜score on quiz)

Q8: The strength of the above relationship is considered?
Answer: Strong (C)

Part B** Compute the regres...

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Review

Anonymous
Awesome! Exactly what I wanted.

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