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Stat 200 HOMEWORK 7
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Lane Chap. 14

2. The formula for a regression equation is Y’ = 2X + 9.

a. What would be the predicted score for a person scoring 6 on X?

The predicted score for that person would be,

Y = 2*6+9 = 21

b. If someone’s predicted score was 14, what was this person’s score on X?

In this case Y = 14 thus,

14 = 2X+9

  • X = (14-9)/2 = 2.5

Thus the score on X was 2.5.

 

6. For the X, Y data below, compute:

a. r and determine if it is significantly different from zero.

The obtained output from Minitab is given below,

Correlation: X, Y

 

Pearson correlation of X and Y = 0.849

P-Value = 0.032

 

From the above output we can see that the correlation coefficient between X and Y is 0.849 with corresponding P value 0.032. As the P value is smaller than the significance level of 0.05 so we can conclude that the correlation coefficient is significantly different from zero.

b. the slope of the regression line and test if it differs significantly from zero.

Using the data analysis tool pack of Excel the obtained output is given below,

SUMMARY OUTPUT

           
             

Regression Statistics

         

Multiple R

0.8492

         

R Square

0.7211

         

Adjusted R Square

0.6514

         

Standard Error

3.5028

         

Observations

6

         
             

ANOVA

           

 

df

SS

MS

F

Significance F

 

Regression

1

126.9207

126.9207

10.3441

0.0324

 

Residual

4

49.0793

12.2698

     

Total

5

176

 

 

 

 
             

 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

3.1231

3.1085

1.0047

0.3719

-5.5075

11.7537

X

1.1332

0.3523

3.2162

0.0324

0.1550

2.1115

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