Self Test 8 for Probability and Statistics

Curve Fitting, Regression and Correlation

This test was constructed by Zauresh Atakhanova based on the Schaum's Outline Theory and Problems of Probability and Statistics by Murray R. Spiegel. If you need more review refer also to this outline.

The least-squares line

1.True False. Given the following data, fit a least-square line using (a) x as independent variable, (b) x as dependent variable.

 x 1 3 4 6 8 9 11 14 y 1 2 4 4 5 7 8 9

a)      y=0.345 + 0.036x

b)      x=-0.5 + 1.5y

2.True False. The least squares line always passes through the point (`x,`y).

## Non-linear equations reducible to linear form

3. True False. The following table gives experimental values of the pressure P of a given mass of gas corresponding to various values of the volume V. According to thermodynamic principles a relationship having the form PVg=C, where g and C are constants, should exist between the variables. (a) The values of g and C are C=17,154.22 and g=1.42. (b) The equation connecting P and V is PV1.42=17,154.22. (c) The estimate P when V=150 in3 is 13.95.

 V (in3) 54.2 61.7 72.3 88.6 118.6 193.9 P (lb/in2) 61.1 49.4 37.5 28.3 19.1 10

## Standard error of the estimate

4.True False. The standard error of estimates, sy.x for the data of problem 1 is 0.4156

5.True False. For the data of problem 1.The explained variation is 43.3933, (b) the unexplained variation is 3.5455 and (c) the total variation is 49

## The linear correlation coefficient

6.True False The coefficient of rank correlation for the data of problem 1 is 0.9940.

## Sampling theory of regression

7.True False. In problem 1 you found the regression equation to be y=0.545 + 0.636x. For this equation, we fail to that the regression coefficient of the population regression equation is as low as 0.454at the 5% significance level.

8.True False. The 95% confidence limits for the regression coefficient of problem 7 are 0.636 +/-0.0387