Question

After you run the Regression, answer these questions (type responses in this box):

1. What is the p-value (the significance)?

2. Is the relationship between Hours in Therapy and Depression Inventory Score statistically significant?

3. Do Depressions Scores increase or decrease as a result of having more Hours in Therapy?

REGRESSION
Hours in Therapy	Depression Inventory Score
9	20
9	28
9	20
9	26
11	19
11	15
13	12
13	11
15	10
15	11
16	10
16	8
17	13
17	14
18	10
18	10
21	8
21	9
21	7
21	8
21	8
21	9
22	11
22	10
22	8
22	8
23	10
23	10
24	8
24	10
25	6
25	5
25	4
25	10
27	6
27	6
31	7
31	6
36	10
36	7

Answer 1

Note that Depression inventory score depends on Hours in therapy. So,

Independent variable(X): Hours in therapy.

Dependent variable(Y) : Depression inventory score.

We will fit regression equation using R software.

R software codes

>x=c(9,9,9,9,11,11,13,13,15,15,16,16,17,17,18,18,21,21,21,21,21,21,22,22,22,22,23,23,24,24,25,25,25,25,27,27,31,31,36,36)

>y=c(20,28,20,26,19,15,12,11,10,11,10,8,13,14,10,10,8,9,7,8,8,9,11,10,8,8,10,10,8,10,6,5,4,10,6,6,7,6,10,7)

>model=lm(y~x)

>summary(model)

Data vectors x and y are created. lm() function is used to fit the regression equation. summary() function is used to get the summary of the fitted regression model.

R software output

1. Observe the above output.

p-value is 5.824×10^-08.

2. We test,

Null hypothesis Ho: The fitted regression model is significant.

Vs

Alternative hypothesis H₁: Fitted regression model is not significant.

We reject null hypothesis if p-value is less than the given level of significance. Here p-value is 5.824×10^-08 which is very less than the level of significance 0.05 or 0.01 so we reject null hypothesis. Which implies that the Fitted regression model is significant which in turn implies that the relationship between Hours in Therapy and Depression inventory score is statistically significant.

3. Observe the above output. Fitted regression equation is

Depression inventory score= 22.06644 - 0.55992(Hours of therapy) .

Coefficient associated with Hours of therapy is negative which implies that Depression inventory score decreases as a result of more hours in therapy.

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