The following sample observations were randomly selected Do

The following sample observations were randomly selected. (Do not round the intermediate values. Round your answers to 2 decimal places.)

X:

4

5

3

6

10

Y:

9.7

5

9.9

16.3

23.5

Determine the 0.95 confidence interval for the mean predicted when
X = 5 ( , )

Determine the 0.95 prediction interval for an individual predicted when
X = 5 ( , )

The following sample observations were randomly selected. (Do not round the intermediate values. Round your answers to 2 decimal places.)

Solution

The following sample observations were randomly selected. (Do not round the intermediate values. Round your answers to 2 decimal places.)

X:

4

5

3

6

10

Y:

9.7

5

9.9

16.3

23.5

Regression Analysis

r²

0.718

n

5

r

0.847

k

1

Std. Error

4.394

Dep. Var.

Y

ANOVA table

Source

SS

df

MS

F

p-value

Regression

147.6451

1  

147.6451

7.65

.0698

Residual

57.9229

3  

19.3076

Total

205.5680

4  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=3)

p-value

95% lower

95% upper

Intercept

0.2877

4.9596

0.058

.9574

-15.4959

16.0713

X

2.2486

0.8132

2.765

.0698

-0.3392

4.8365

Predicted values for: Y

95% Confidence Interval

95% Prediction Interval

X

Predicted

lower

upper

lower

upper

Leverage

5

11.5308

5.0872

17.9744

-3.8662

26.9278

0.212

a.

Determine the 0.95 confidence interval for the mean predicted when
X = 5 (5.09 , 17.97 )

b.

Determine the 0.95 prediction interval for an individual predicted when
X = 5    (-3.87 , 26.93)

The following sample observations were randomly selected. (Do not round the intermediate values. Round your answers to 2 decimal places.)