Question

Let x be a random variable that represents blood glucose level after a 12-hour fast. Let y be a random variable representing blood glucose level 1 hour after drinking sugar water (after the 12-hour fast). Units are in milligrams per 10 milliliters (mg/10 ml). A random sample of eight adults gave the following information.

Σx = 63.8; Σx² = 521.84; Σy = 89.7; Σy² = 1045.43; Σxy = 730.74

x	6.2	8.3	7.0	7.5	8.1	6.9	10.0	9.8
y	9.6	10.3	10.8	11.5	14.2	7.0	14.1	12.2

(a) Find the equation of the least-squares line. (Round your answers to three decimal places.)
ŷ = ? +__________
.

(c) Find the sample correlation coefficient r and the sample coefficient of determination

r².

(Round your answers to three decimal places.)

r =
r2 =

(d) If

x = 8.0,

use the least-squares line to predict y. (Round your answer to two decimal places.)

y = 9

Find an 80% confidence interval for your prediction. (Round your answers to two decimal places.)

lower limit	10 mg/10 ml
upper limit	11 mg/10 ml

(e) Use level of significance 1% and test the claim that the population correlation coefficient ρ is not zero. (Round your test statistic to three decimal places.)

t = 12

Find or estimate the P-value of the test statistic.

P-value > 0.500 0.250 < P-value < 0.500     0.200 < P-value < 0.250 0.150 < P-value < 0.200 0.100 < P-value < 0.150 0.050 < P-value < 0.100 0.020 < P-value < 0.050 0.010 < P-value < 0.020 0.001 < P-value < 0.010 P-value < 0.001

Conclusion

(f) Find an 85% confidence interval for the slope β of the population-based least-squares line. (Round your answers to three decimal places.)

lower limit
upper limit

Answer 1

Answer a) ŷ = 1.801 + 1.18*x

Answer c)

Correlation Coefficient (r) Calculation

Correlation Coefficient r = 0.6765

Coefficient of Determination r2 = 0.6765*0.6765 = 0.4577

Answer d) Predicted y = 11.24

For x = 8, we can predict y using regression line equation:

ŷ = 1.801 + 1.18*x

ŷ = 1.801 + 1.18*8

ŷ = 11.241

80% confidence interval for prediction calculation

Now, we are going to compute the 80% confidence interval for the mean response value ŷ =11.241. The first step consists of finding the standard error of the estimate, for which we need to deal with the regression sum of squares and with the sum of squared errors.

So, confidence interval for prediction is (10.27, 12.21)

Answer e) Test Statistics = 2.25

Correlation Coefficient Significance Calculator using p-value

The following needs to be tested:

H0​: ρ = 0

HA​​: ρ ≠ 0

where ρ corresponds to the population correlation.

This is not enough evidence to claim that the population correlation coefficient ρ is not zero.

We can answer 4 parts only.