Question
In: Statistics and Probability
Run a regression analysis on the following bivariate set of data with y as the response...
Run a regression analysis on the following bivariate set of data with y as the response variable.
| x | y |
|---|---|
| 81 | 81.3 |
| 92.6 | 90.8 |
| 80.1 | 94.9 |
| 77.8 | 53.4 |
| 89.4 | 102.9 |
| 70.3 | 38.2 |
| 90.2 | 98 |
| 81.4 | 94.6 |
| 94.9 | 122.4 |
| 77.2 | 42.1 |
| 70.6 | 47.8 |
| 71 | 50.6 |
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. (If the answer is
0.84471, then it would be 84.5%...you would enter 84.5 without the
percent symbol.)
r² = %
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 95.7 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 response value? (Report answer accurate to
one decimal place.)
y =
Solutions
Expert Solution
| correlation coefficient r= | Sxy/(√Sxx*Syy) = | 0.881 | |
r² = 0.881^2*100 = 77.7 %
3)
| sample size n= | 12 | |
| y̅ = | 76.4167 | |
| x̅ = | 81.3750 | |
| Sxx= | Σ(Xi-X̅)2= | 829.583 |
| Sxy = | Σ(Xi-X̅)(Yi-Y̅)= | 2386.435 |
| slope= β̂1 = | Sxy/Sxx= | 2.8767 |
| intercept= β̂0 = | y̅-β1x̅= | -157.6723 |
| Least square line equation: ŷ =2.877*x +(-157.672) | ||
4)
| predicted val=-157.672+95.7*2.877= | 117.7 (please try 117.6 if this comes wrong) | |
orchestra answered 2 years agoRelated Solutions
Run a regression analysis on the following bivariate set of data with y as the response...
Run a regression analysis on the following bivariate set of data
with y as the response variable.
x
y
15.5
58.8
25.4
62.9
53.7
68.8
46.5
78.6
28.5
57.5
5.7
68.1
-0.4
67.8
43.8
87.7
23.1
64.9
31.3
81.3
48.2
80.1
15.9
71.1
1) Find the correlation coefficient and report it accurate to
three decimal places.
r =
2) What proportion of the variation in y can be
explained by the variation in the values of x? Report
answer as...
Run a regression analysis on the following bivariate set of data with y as the response...
Run a regression analysis on the following bivariate set of data
with y as the response variable.
x
y
73
16.1
80
14.9
72.5
8.5
55.8
33.6
54.6
23.4
76.6
26.2
74.6
19.1
40.2
40.6
58.7
25.8
Find the correlation coefficient and report it accurate to three
decimal places.
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...
Run a regression analysis on the following bivariate set of data with y as the response...
Run a regression analysis on the following bivariate set of data
with y as the response variable. x y 26.1 54.3 28.4 42.5 33.8 50.2
63.4 63.3 64.3 79.4 72.5 76.1 46.2 57.4 70.2 82.1 50.5 64.3 55.4
58.8 40.7 48.5 69.4 57.5 40.4 47.8 45.1 60 64 72.5 50.6 56.9 44.2
65.6 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...
Run a regression analysis on the following bivariate set of data with y as the response...
Run a regression analysis on the following bivariate set of data
with y as the response variable.
x
y
58.6
56.3
66.3
72.1
54.8
119.2
57.4
83.2
62.8
74.3
77.6
72.2
71.8
62.2
46.4
77.2
77.4
86.6
60.5
78.4
66.4
131.3
76.4
113.5
68.5
84.2
81.5
102
77.5
136.3
49
12.2
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...
Run a regression analysis on the following bivariate set of data with y as the response...
Run a regression analysis on the following bivariate set of data
with y as the response variable. x y 37.2 26.9 66.2 41.4 80.9 37.6
83.7 45 55 31.2 46.3 29.1 82 44.1 71.6 36.1 54.7 29.3 56.4 33.8
Predict what value (on average) for the response variable will be
obtained from a value of 45.1 as the explanatory variable. Use a
significance level of α = 0.05 to assess the strength of the linear
correlation. What is the predicted...
Run a regression analysis on the following bivariate set of data with y as the response...
Run a regression analysis on the following bivariate set of data
with y as the response variable.
x
y
62.4
39.2
62.2
40.4
47.7
68.9
120.5
-36.5
49
37.9
69.1
-9.4
53.2
71.8
66
13.8
87
8.4
92.3
-1.6
70.3
17.8
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 67.7
on the response variable.
What is the predicted...
a) Run a regression analysis on the following bivariate set of data with y as the...
a) Run a regression analysis on the following bivariate set of
data with y as the response variable.
x
y
10.7
81.6
13.7
81.5
36.7
56.5
4
72.1
50.7
23.2
47.6
-4.8
37.3
31.9
24.3
75.2
21.5
59.3
17.2
54.6
23.6
75.5
22.2
60.8
29.3
51
14
63.4
0.2
102.7
30.7
48.2
10.3
74.8
26.5
48.2
23.1
87
Verify that the correlation is significant at an ?=0.05?=0.05.
If the correlation is indeed significant, predict what value (on
average) for the...
8. Run a regression analysis on the following bivariate set of data with y as the...
8. Run a regression analysis on the following bivariate set of
data with y as the response variable.
x
y
27.2
68.2
28.1
66.7
28.7
64.6
30.2
66.4
33.7
69.5
31.8
68.3
30.4
67.8
28.6
65.5
32.5
69.4
34.8
67.9
33.3
67.1
28
66.1
- 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...
Using your calculator, run a regression analysis on the following bivariate set of data with y...
Using your calculator, run a regression analysis on the
following bivariate set of data with y as the response
variable.
x y
71.2 23.1
90.8 122.9
88.8 82.9
57.7 18.3
71.4 8.6
60.4 25.9
60.2 -43.1
88.5 77.4
68.2 -5.9
41.1 -83
61.4 -2.5
87.1 39.4
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...
You run a regression analysis on a bivariate set of data (n=99). You obtain the regression...
You run a regression analysis on a bivariate set of data (n=99).
You obtain the regression equation
y=0.843x+6.762
with a correlation coefficient of r=0.954 which is significant
at α=0.01 You want to predict what value (on average) for the
explanatory variable will give you a value of 150 on the response
variable.
What is the predicted explanatory value?
x =
(Report answer accurate to one decimal place.)
Here is a bivariate data set. Find the regression equation for
the response...
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