**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).

**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 PV^{g}=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 PV^{1.42}=17,154.22.
(c) The estimate P when V=150 in^{3 }is^{ }13.95.

V (in |
54.2 |
61.7 |
72.3 |
88.6 |
118.6 |
193.9 |

P (lb/in |
61.1 |
49.4 |
37.5 |
28.3 |
19.1 |
10.0 |

**4.True False.** The standard error of estimates, s_{y.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

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

**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