Physical properties of six flame-retardant fabric samples were investigated in a

Question

Physical properties of six flame-retardant fabric samples were investigated in an article. Use the accompanying data and a 0.05 significance level to determine whether a linear relationship exists between stiffness x (mg-cm) and thickness y (mm).

Compute the value of the sample correlation coefficient, r. Round your answer to four decimal places.

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.)

x   7.93 24.39 12.42 6.72 24.12 35.84 y   0.28 0.64 0.32 0.27 0.82 0.58

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = 0.19708631 + 0.015504237 x
Sample size: 6
R (correlation coefficient) = 0.77670134
R-sq = 0.60326497
Estimate of error standard deviation: 0.16081718

Parameter estimates:

Analysis of variance table for regression model:

Hence,

r = 0.7767

Test statistic = 2.47

P - value = 0.069

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 0.19708631 0.13393709 0 4 1.4714842 0.2151 Slope 0.015504237 0.0062866117 0 4 2.4662311 0.0692

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