Question

1. Here is a bivariate data set.

x | y |
---|---|

49.7 | 34.8 |

43.9 | 30.9 |

48 | 30 |

46.3 | 32 |

46.9 | 30.3 |

46.2 | 34.6 |

Find the correlation coefficient and report it accurate to three
decimal places.

*r* =

What proportion of the variation in *y* can be explained by
the variation in the values of *x*? Report answer as a
percentage accurate to one decimal place.

*r*² = %

2. You run a regression analysis on a bivariate set of data (n=71). With ¯x=58.8 and ¯y=34.3, you obtain the regression equation

y=−0.996x+3.479

with a correlation coefficient of r=−0.206r=-0.206. You want to
predict what value (on average) for the response variable will be
obtained from a value of 20 as the explanatory variable.

What is the predicted response value?

*y* =

(Report answer accurate to one decimal place.)

3.Match each scatterplot shown below with one of the four
specified correlations.

- -abcd
- -abcd
- -abcd
- -abcd

Answer #1

1.

x |
y |
XY |
X² |
Y² |

49.7 | 34.8 | 1729.56 | 2470.09 | 1211.04 |

43.9 | 30.9 | 1356.51 | 1927.21 | 954.81 |

48 | 30 | 1440 | 2304 | 900 |

46.3 | 32 | 1481.6 | 2143.69 | 1024 |

46.9 | 30.3 | 1421.07 | 2199.61 | 918.09 |

46.2 | 34.6 | 1598.52 | 2134.44 | 1197.16 |

Ʃx = | Ʃy = | Ʃxy = | Ʃx² = | Ʃy² = |

281 |
192.6 |
9027.26 |
13179.04 |
6205.1 |

Sample size, n = | 6 |

x̅ = Ʃx/n = | 46.8333 |

y̅ = Ʃy/n = | 32.1 |

SSxx = Ʃx² - (Ʃx)²/n = | 18.8733 |

SSyy = Ʃy² - (Ʃy)²/n = | 22.64 |

SSxy = Ʃxy - (Ʃx)(Ʃy)/n = | 7.16 |

Correlation coefficient, r = SSxy/√(SSxx*SSyy) =
**0.346**

Coefficient of determination, r² = (SSxy)²/(SSxx*SSyy) = 0.1200
= **12%**

-----------------------------------

2. y = −0.996 x + 3.479

At x = 20, predicted y =

y = −0.996 * 20 + 3.479 = **-16.4**

Here is a bivariate data set.
x
y
15.9
16.9
83.4
53.9
43.8
22.2
49.4
49.3
58.4
11.8
77.4
38.8
19.6
19.5
Find the correlation coefficient and report it accurate to three
decimal places.
r =
What proportion of the variation in y can be explained by
the variation in the values of x? Report answer as a
percentage accurate to one decimal place.
r² = %
2. Run a regression analysis on the following bivariate set of
data with...

1. Here is a bivariate data set.
x
y
83.7
47.7
73.3
55.5
68.5
42.3
59
43.5
67
41.8
61.6
40.8
64.3
39.2
99.7
71.7
60.8
34.7
69.8
44
86
59.4
47.3
30.8
37.6
20.8
58.6
37.4
57.3
41.1
Find the correlation coefficient and report it accurate to three
decimal places.
r =
2.Run a regression analysis on the following bivariate set of
data with y as the response variable.
x
y
3.8
74.8
54.7
49.8
26.5
64.7
-7.8
86.8...

Run a regression analysis on the following bivariate set of data
with y as the response variable.
x
y
48
41.8
39.2
67.4
34.7
68.4
42.9
50.2
49
50.6
45.6
57
58.7
29.7
40.5
68.4
47.4
34.7
45.7
50.9
38.9
47.7
40.9
53.6
Find the correlation coefficient and report it accurate to three
decimal places.
r =
What proportion of the variation in y can be explained by
the variation in the values of x? Report answer as a
percentage...

Run a regression analysis on the following bivariate set of data
with y as the response variable.
x
y
81.1
86
77.5
60.4
92.7
126.5
104
132.5
85
53.1
64.3
95.5
64.6
31.7
39.7
5.7
82.3
121.3
82.4
98.2
29.2
-50.2
34.2
-1
Find the correlation coefficient and report it accurate to three
decimal places.
r =
What proportion of the variation in y can be explained by
the variation in the values of x? Report answer as a
percentage...

Run a regression analysis on the following bivariate set of data
with y as the response variable.
x
y
28.8
90.1
30.6
139.6
12.6
42.2
18.1
94.8
13.9
28.5
31.9
102.4
-3.9
-13.4
16.7
57.1
11
55.8
16.8
76.3
31.7
80.1
43.5
123.8
Find the correlation coefficient and report it accurate to three
decimal places.
r =
What proportion of the variation in y can be explained by
the variation in the values of x? Report answer as a
percentage...

Run a regression analysis on the following bivariate set of data
with y as the response variable.
x
y
51.3
17.4
60.8
88.6
37.4
32.9
44.6
53.4
53.7
53.6
52.2
41.5
32.7
28.6
62.4
84.7
47.4
35.7
39.8
33.7
62.1
123
62
83.7
Find the correlation coefficient and report it accurate to three
decimal places.
r = _______
What proportion of the variation in y can be explained by
the variation in the values of x? Report answer as a...

Here is a bivariate data set.
x
y
39.1
42.5
17.1
215.1
28.7
109.5
55.4
18.5
19.9
186.9
9.8
31.2
62.7
-41.6
61.9
-16.5
58.4
-31.2
63.3
-120.1
67.1
124.8
Find the correlation coefficient and report it accurate to three
decimal places.
r =
What proportion of the variation in y can be explained by
the variation in the values of x? Report answer as a
percentage accurate to one decimal place.
r² = %

Run a regression analysis on the following bivariate set of data
with y as the response variable.
x
y
31
131.5
32.7
88.1
45.9
52.1
51.8
47
65.8
30.1
58.4
36.4
84.5
-92.1
25.3
103.4
49.8
37.5
4.6
127.3
46.6
32.1
75.2
-12.4
Find the correlation coefficient and report it accurate to three
decimal places.
r =
What proportion of the variation in y can be explained by
the variation in the values of x? Report answer as a
percentage...

Run a regression analysis on the following bivariate set of data
with y as the response variable.
x
y
69
25.6
87.1
99.4
80.3
77.2
100.4
148
38.1
4.6
99.7
116.2
82.7
74.6
98
100.3
78.5
65.9
93.4
117.5
82.7
106.4
85
52.3
Find the correlation coefficient and report it accurate to three
decimal places.
r =
What proportion of the variation in y can be explained by
the variation in the values of x? Report answer as a
percentage...

Here is a bivariate data set.
x
y
38.3
58.8
38.7
59.5
51.1
39.4
43.8
54
51.2
46.1
45.8
54.9
38.3
55.2
31.7
59.7
35.5
52.3
19.1
70.8
31.9
63.8
50.1
51.7
52.1
48.9
Find the correlation coefficient and report it accurate to three
decimal places.
r = _____

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