Question

Does the number of years that a woman is on birth control (X)
have an effect on how long it takes for her to become pregnant (Y)
once she ceases to use it and tries to have children? A curious
researcher collected the following data for a sample of pregnant
women who had previously used birth control:

Years on Birth Control (X) |
Time Until Pregnant (Y) |

7.5 | 25 |

10.0 | 31 |

3.5 | 42 |

4.0 | 36 |

7.0 | 13 |

2.5 | 22 |

5.0 | 56 |

a) Draw a scatter plot of the data

b) Calculate the regression slope and Y-intercept

c) Draw a regression line on the scatter plot

d) Can you predict how long it will take for a woman who was on
birth control for eight years to get pregnant once she stops using
it?

e) Find the coefficients of determination and nondetermination.
What do they mean?

f) Construct an analysis of variance table and perform an F test on
the significance of the regression.

Answer #1

a.

b.

c.

d.

f.

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 39.577 14.292 2.769 0.0394 *

x -1.317 2.324 -0.567 0.5953

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 15.03 on 5 degrees of freedom

Multiple R-squared: 0.06039, Adjusted R-squared: -0.1275

F-statistic: 0.3214 on 1 and 5 DF, p-value: 0.5953

Df Sum Sq Mean Sq F value Pr(>F)

x 1 72.65 72.646 0.3214 **0.5953**

Residuals 5 1130.21 226.042

Since p-value=0.5953>0.05, hence regression equation of Y on X is not significant at 5% level.

Suppose that a researcher collected the following set of data
on years of education (X) and number of children for a sample of
married adults:
X
Y
12
2
14
1
17
0
10
3
8
5
9
3
12
4
14
2
18
0
16
2
Draw a scatter plot of the data.
Write out the regression equation, then calculate and
interpret the meaning of the...

This same researcher collected at random one child from each of
the eight families in which there was at least one child. She
recorded the following data to study the effects of number of
siblings (X) on happiness of the child (Y), measured on an interval
scale in which low scores indicate a low level of happiness and
high scores indicate a high level of happiness:
X
Y
1
5
0
3
2
4
...

1) Generate a data set with three variables (X, Y and Z). X and
Y have 10 observations for each (N=10), and Z has 13 observations
(N=13). Each observation should have two digits (such as “83” or
“8.3”).
2) Draw a stem-and-leaf display for variable Z only and draw a
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A clothing department wants to find out if there is a
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$17
9
$63...

Let x be the age in years of a licensed automobile
driver. Let y be the percentage of all fatal accidents
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to speeding.
x 17 27 37 47 57 67 77
y 37 23 18 12 10 7 5
Complete parts (a) through (e), given Σx = 329,
Σy = 112, Σx2 = 18,263,
Σy2 =...

Let x be the age of a licensed driver in years. Let
y be the percentage of all fatal accidents (for a given
age) due to failure to yield the right of way. For example, the
first data pair states that 5% of all fatal accidents of
37-year-olds are due to failure to yield the right of way.
x
37
47
57
67
77
87
y
5
8
10
16
32
42
Complete parts (a) through (e), given Σx =...

The accompanying data represent the number of days absent, x,
and the final exam score, y, for a sample of college students in a
general education course at a large state university. Complete
parts (a) through (e) below.
Absences and Final Exam Scores
No. of absences, x
0
1
2
3
4
5
6
7
8
9
Final exam score, y
89.6
87.3
83.4
81.2
78.7
74.3
64.5
71.1
66.4
65.6
Critical Values for Correlation Coefficient
n
3
0.997
4...

Let x be the age in years of a licensed automobile
driver. Let y be the percentage of all fatal accidents
(for a given age) due to speeding. For example, the first data pair
indicates that 34% of all fatal accidents of 17-year-olds are due
to speeding.
x
17
27
37
47
57
67
77
y
34
28
18
12
10
7
5
Complete parts (a) through (e), given
Σx = 329, Σy = 114,
Σx2 = 18,263,
Σy2 =...

A sociologist is interested in the relation between x =
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x
(number of job changes)
4
3
5
6
1
5
9
10
10
3
y
(Salary in $1000)
38
34
31
32
32
38
43
37
40
33
In this setting we have ?x = 56,...

Applications I
Consider the following data representing the total time (in hours)
a student spent on reviewing for the Stat final exam and the actual
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time score
0 23
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7 50
8 45
10 55
12 60
15 70
18 80
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