Question

In the counseling literature, it appears that one thing that is important in counseling is the amount of empathy that a therapist displays towards a client. After reading this literature, a counseling psychologist is interested in the role of empathy specifically on clients with anxiety. In order to predict the change in anxiety based on a counselor’s empathy, the counselor observes several therapists and clients during counseling sessions. The researcher measures the amount of time that therapist displays empathy toward the client. In addition, the counselor measures the amount of anxiety symptoms the client displays over the course of a week. Use the following data to create a data file and to answer the questions below.

Empathy in seconds	Anxiety Symptoms
354	5
607	2
132	13
276	2
286	12
543	4
389	8
201	13
378	9
645	2
321	10
276	14
391	9
462	4
357	5
422	7
102	17
328	8
357	6
486	3

Questions:

1. Report the Standard Error of Estimate.
2. Report the Regression Equation.
3. Given the equation above, what would be the CPWi for a child whose parents scored a 115 on the MSS?

Answer 1

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	7313.00	153.00	373350.55	374.55	-9533.45
mean	365.65	7.65	SSxx	SSyy	SSxy

SSE=   (SSxx * SSyy - SS²xy)/SSxx =    131.1148
std error ,Se =    √(SSE/(n-2)) =    2.6989

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

b)

Sample size,   n =   20      
here, x̅ = Σx / n=   365.650          
ȳ = Σy/n =   7.650          
SSxx =    Σ(x-x̅)² =    373350.5500      
SSxy=   Σ(x-x̅)(y-ȳ) =   -9533.5      
              
estimated slope , ß1 = SSxy/SSxx =   -9533.45/373350.55=   -0.0255      
intercept,ß0 = y̅-ß1* x̄ =   7.65- (-0.0255 )*365.65=   16.9868      
              
Regression line is, Ŷ=   16.987   + (   -0.026   )*x
.....

c)

Predicted Y at X=   115   is          
Ŷ=   16.98682   +   -0.02553   *115=   14.050 ~ 14

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

Please let me know in case of any doubt.

Thanks in advance!

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