Hi guys,

I have a question that I have done a bit of...

just need checking

and if sumone can tell me how to do the rest...coz im confused

thanks

A chemist is interested in determining the weight loss y (in pounds) of a particular compound as a function of the amount of time x (in hours) the compound is exposed to the air.

A regression model y = βo + B1 + ε is fitted to the data observed, where ε is the random error term

having a standard deviation σ. An incomplete Minitab output is given below where C1 represents

the y variable and C2 represents the x variable.

The regression equation is

C1 = 1.44 + 0.720 C2

Predictor Coef SE Coef T P

Constant 1.440 1.346 1.07 0.3100

C2 0.7200 0.2398 ? ?

S = ??? R-Sq = ??? R-Sq(adj) = 42.2%

Analysis of Variance

Source DF SS MS F P

Regression 1 ??? 7.7760 ??? 0.013

Residual Error 10 8.6240 ???

Total 11 16.4000

Predicted Values for New Observations

New Obs Fit SE Fit 95.0% CI 95.0% PI

1 5.040 0.294 ( ??, ??) ( ??, ??)

Values of Predictors for New Observations

New Obs C2

1 5.00

(a) Calculate R2(i.e., R-Sq) — the proportion of the total variation in weight loss y observations that can be explained by x observations.

r2 = SSTO - SSE / SSTO

=16.4 - 8.624/16.4

=.474

=47.4%

(b) Calculate a 90% confidence interval for

1, the slope of the regression model.

b1 ± t* s.e. (b1)

= 0.72 ±1.81 x 0.2398

= 0.72 ± 0.434

= 0.286 to 1.154

(c) State and test the hypothesis about whether the slope

1 is different from 0. Use significance level

= 0.01 in the test. List H0 and Ha, the test statistic, the p-value and the conclusion.

Ho: β¹ ≠ 0

H1: β¹ = 0

T = ( b1 - 0 )/(s.e(b1)

=0.72-0/0.2398

=3.0025

(d) Find the fitted value of weight loss when the exposure time is 5 hours.

(e) Calculate a 95% confidence interval for the mean weight loss when the exposure time is 5

hours?

(f) Find the value of s — an estimate of — using the Minitab output supplied.

(g) Calculate a 95% prediction interval for the weight loss when the exposure time is 5 hours?