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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!
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Explanation & Answer
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 =
∑ 𝑥 11
=
= 2.75
𝑛
4
∴ SXY =
𝑌̅ =
∑ (𝑋𝑖 − 𝑋̅)(𝑌𝑖 − 𝑌̅)
𝑛−1
∑ 𝑦 22
=
= 5.50
𝑛
4
(1 − 2.75)(3 − 5.50) + (2 − 2.75)(5 − 5.50) + (3 − 2.75)(5 − 5.50) + (5 − 2.75)(9 − 5.50)
n−1
SXY =
(−1.75)(−2.5) + (−0.75)(−0.5) + (0.25)(−0.5) + (2.25)(3.5)
4−1
SXY =
4.375 + 0.375 − 0.125 + 7.875 12.5
=
= 4.1667
3
3
Answer: The covariance is 4.1667
Alternatively:
COV(X, Y) =
∑ 𝑋𝑌 − 𝑌̅ ∑ 𝑋 − 𝑋̅ ∑ 𝑌 + 𝑛𝑋̅𝑌̅ 73 − (5.5)(11) − 2.75(22) + 4(2.75)(5.5) 12.5
=
=
𝑛−1
4−1
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:
̅ ∑ 𝑋 + 𝑛𝑋
̅2
∑ (𝑋𝑖 − 𝑋̅)2
∑ 𝑋2 − 2𝑋
√
𝑆𝑋 = √
=
𝑛−1
𝑛−1
39 − 2(2.75)(11) + 4(2.752 )
8.75
∴ 𝑆𝑋 = √
=√
= 1.7078
4−1
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:
∑ (𝑌𝑖 − 𝑌̅)2
∑ 𝑌2 − 2𝑌̅ ∑ 𝑌 + 𝑛𝑌̅ 2
√
√
𝑆𝑌 =
=
𝑛−1
𝑛−1
140 − 2(5.50)(22) + 4(5.502 )
19
√
∴ 𝑆𝑌 =
= √ = 2.5166
4−1
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:
𝑟=
𝑛 ∑ 𝑥𝑦 − ∑ 𝑥 ∑ 𝑦
√[𝑛 ∑ 𝑥 2 − (∑ 𝑥)2 ][𝑛 ∑ 𝑦 2 − (∑ 𝑦)2 ]
Alternatively, r can be computed from the standard deviation as:
𝑟=
∴𝑟=
𝑆𝑋𝑌
𝑆𝑋 ∙ 𝑆𝑌
4.1667
= 0.9695
1.7078 × 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 ‘hours studied’ goes up, there is a corresponding increase in ‘score on quiz)
Q8: The strength of the above relationship is considered?
Answer: Strong (C)
Part B** Compute the regres...
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