Question

In: Statistics and Probability

In the counseling literature, it appears that one thing that is important in counseling is the...

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?

Solutions

Expert Solution

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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