In preparation of plastic molds, the hardness of the mold mainly depends on elap
ID: 3249724 • Letter: I
Question
In preparation of plastic molds, the hardness of the mold mainly depends on elapsed time since preparation of the test sample among other factors. Twelve batches of test samples were observed over a predetermined levels of elapsed times X (measured in hours) with respect to their hardness Y (in Brinell units). The data are summarized below: (i) Obtain the estimated linear regression function. (ii) Obtain a point estimate of the change in mean hardness when X increases by 5 hours. (iii) Provide the value of the multiple correlation and comment on it as a measure of goodness of fit of the linear model for this data.Explanation / Answer
We have excel output as :
i) The regression equation is given by
y = a + b x
Where a= intercept = 166.8
b = slope = 2.11
Hence the required regression equation is
y = 166.8 + 2.11 * x
ii) Here we have x = 5
y = 166.8 + 2.11 * 5 = 177.35
Point estimate for change in mean hardness is 177.35
iii) Multiple correlation = R = 0.99
Hence we conclude that there is extremely strong relation between levels of elapsed time nad hardness.
Regression Statistics Multiple R 0.990938 R Square 0.981959 Adjusted R Square 0.980155 Standard Error 2.8 Observations 12 ANOVA df SS MS F Significance F Regression 1 4267.267 4267.267 544.2942 4.74E-10 Residual 10 78.4 7.84 Total 11 4345.667 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 166.8 2.656313 62.7938 2.55E-14 160.8814 172.7186 x 2.108333 0.09037 23.33011 4.74E-10 1.906977 2.309689