Question

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 accurate to one decimal place. (If the answer is
0.84471, then it would be 84.5%...you would enter 84.5 without the
percent symbol.)

*r*² = %

Based on the data, calculate the regression line (each value to
three decimal places)

y = x +

Predict what value (on average) for the response variable will be
obtained from a value of 87 as the explanatory variable. Use a
significance level of α=0.05 to assess the strength of the linear
correlation.

What is the predicted response value? (Report answer accurate to
one decimal place.)

*y* =

Answer #1

The given data is inputted in EXCEL, post which the SCATTERPLOT function is used to obtain the scatter plot and then the TRENDLINE function is used to obtain the regression equation here as:

The correlation coefficient now is computed here as:

**Therefore 0.903 is the required correlation coefficient
here.**

As the coefficient of determination here is 0.8156, therefore
**81.56% of the variation in the in y can be explained by the
variation in x here.**

The regression equation can be seen from the plot here as:

Now the predicted value here is computed as:

**Therefore 100.7 is the required predicted value
here.**

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
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
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...

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...

Run a regression analysis on the following bivariate set of data
with y as the response variable.
x
y
16.1
47.3
10.6
42.8
22.4
50.6
33.3
67.6
47.8
61.1
41.4
62.1
30.2
57.9
30.6
53.6
33
57.4
9.7
41.2
19.3
49.6
Verify that the correlation is significant at an α=0.05. If the
correlation is indeed significant, predict what value (on average)
for the explanatory variable will give you a value of 54 on the
response variable.
What is the predicted...

Run a regression analysis on the following bivariate set of data
with y as the response variable.
x
y
107.8
-31.6
73.5
10.7
102
-13.1
44.7
66.8
89.7
2.9
72.7
46.1
76.4
6.7
76.1
22.6
92.2
-0.7
85.4
11.7
98
-8.2
89.8
1.9
66.2
77.1
80.6
21.3
43.4
92.9
Verify that the correlation is significant at an α=0.05α=0.05.
If the correlation is indeed significant, predict what value (on
average) for the explanatory variable will give you a value of -4.3...

Run a regression analysis on the following bivariate set of data
with y as the response variable.
x
y
74.1
53.3
81.3
65.5
64.4
79
102.4
35.8
73
59.4
45.4
110.1
66.4
84.9
73.8
70
52
97.5
70.2
86.9
91.1
43.3
Predict what value (on average) for the response variable will
be obtained from a value of 62.2 as the explanatory variable. Use a
significance level of α=0.05α=0.05 to assess the strength of the
linear correlation.
What is the predicted...

Here is a bivariate data set. Find the regression equation for
the response variable y.
x
y
53.1
41.9
29.1
57.1
49
39
45.6
31.3
29.9
30.2
36.5
27.4
14.2
45.6
44.7
51.3
regression equation:
Enter the equation in slope-intercept form with parameters accurate
to three decimal places.

You run a regression analysis on a bivariate set of data
(n=12n=12). You obtain the regression equation
y=0.631x+48.011y=0.631x+48.011
with a correlation coefficient of r=0.875r=0.875 (which is
significant at α=0.01α=0.01). You want to predict what value (on
average) for the explanatory variable will give you a value of 180
on the response variable.
What is the predicted explanatory value?
x =
(Report answer accurate to one decimal place.)

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