# Statistics question

*label*Mathematics

*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 doesnβt make sense to me. thank you!

## Tutor 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 =

πΜ
=

β π₯ 11

=

= 2.75

π

4

β΄ SXY =

πΜ
=

β (ππ β πΜ
)(ππ β πΜ
)

πβ1

β π¦ 22

=

= 5.50

π

4

(1 β 2.75)(3 β 5.50) + (2 β 2.75)(5 β 5.50) + (3 β 2.75)(5 β 5.50) + (5 β 2.75)(9 β 5.50)

nβ1

SXY =

(β1.75)(β2.5) + (β0.75)(β0.5) + (0.25)(β0.5) + (2.25)(3.5)

4β1

SXY =

4.375 + 0.375 β 0.125 + 7.875 12.5

=

= 4.1667

3

3

Answer: The covariance is 4.1667

Alternatively:

COV(X, Y) =

β ππ β πΜ
β π β πΜ
β π + ππΜ
πΜ
73 β (5.5)(11) β 2.75(22) + 4(2.75)(5.5) 12.5

=

=

πβ1

4β1

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
β π + ππ

Μ
2

β (ππ β πΜ
)2

β π2 β 2π

β

ππ = β

=

πβ1

πβ1

39 β 2(2.75)(11) + 4(2.752 )

8.75

β΄ ππ = β

=β

= 1.7078

4β1

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:

β (ππ β πΜ
)2

β π2 β 2πΜ
β π + ππΜ
2

β

β

ππ =

=

πβ1

πβ1

140 β 2(5.50)(22) + 4(5.502 )

19

β

β΄ ππ =

= β = 2.5166

4β1

3

Answer: The standard deviation of the criterion variable is 2.5166

Q6: What is the Pearsonβs r value?

Solution

The Pearsonβs correlation coefficient, r is given by:

π=

π β π₯π¦ β β π₯ β π¦

β[π β π₯ 2 β (β π₯)2 ][π β π¦ 2 β (β π¦)2 ]

Alternatively, r can be computed from the standard deviation as:

π=

β΄π=

πππ

ππ β ππ

4.1667

= 0.9695

1.7078 Γ 2.5166

Answer: The Pearsonβs r value is 0.9695

Q7: What is the best interpretation of your Pearsonβs correlation in Q6?

Answer:

(A) As βhours studiedβ goes up, there is a corresponding increase in βscore on quiz)

Q8: The strength of the above relationship is considered?

Answer: Strong (C)

Part B** Compute the regres...

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