The following data is representative of that reported in an article with x = bur

Question

The following data is representative of that reported in an article with x = burner-area liberation rate (MBtu/hr-ft2) and y = NOx emission rate (ppm):

(a) Does the simple linear regression model specify a useful relationship between the two rates? Use the appropriate test procedure to obtain information about the P-value, and then reach a conclusion at significance level 0.01.
State the appropriate null and alternative hypotheses.

H0: 1 = 0
Ha: 1 < 0H0: 1 = 0
Ha: 1 > 0    H0: 1 = 0
Ha: 1 0H0: 1 0
Ha: 1 = 0 [Correct]

Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)

(b) Compute a 95% CI for the expected change in emission rate associated with a 10 MBtu/hr-ft2 increase in liberation rate. (Round your answers to two decimal places.)

(_________,_________) ppm

x 100 125 125 150 150 200 200 250 250 300 300 350 400 400 y 160 150 170 220 180 310 270 400 420 430 390 610 610 670

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = -46.484888 + 1.7093298 x
Sample size: 14
R (correlation coefficient) = 0.97846647
R-sq = 0.95739664
Estimate of error standard deviation: 38.37157

Parameter estimates:

Analysis of variance table for regression model:

Predicted values:

Hence,

a) t = 16.42

P - value = 0.000

b) 95% CI:

(-85.25, 26.46)

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept -46.484888 26.592608 0 12 -1.748038 0.106 Slope 1.7093298 0.10409054 0 12 16.421568 <0.0001

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