Question
In: Math
As a researcher, you will be considering the relationships between variables regularly. Linear correlation is the...
As a researcher, you will be considering the relationships between variables regularly. Linear correlation is the most basic relationship that may exist between two variables. This assignment will you give the opportunity to see how statistics can start to answer the research questions you will be faced with in your field of study.
Correlation Project Directions:
Consider a possible linear relationship between two variables that you would like to explore.
- Define the relationship of interest and a data collection technique.
- Determine the appropriate sample size and collect the data.
- Perform the appropriate analysis to determine if there is a statistically significant linear relationship between the two variables. Describe the relationship in terms of strength and direction.
- Construct a model of the relationship and evaluate the validity of that model.
Show all work to receive full credit. Provide complete sentence explanations for each of the above.
Solutions
Expert Solution
Air quality forecasting is very important to identify the variables that control concentration of concerned pollutant and to develop a function F which gives a relationship between the pollutant concentration and the correlated variables. We have a data of AQI and PM10, PM2.5 .
We see there is a relationship between AQI and PM2.5 or AQI and PM10
The data used in this study consists of daily observations of AQI, PM10 and PM2.5 for the period 2017-2019 taken from Central Pollution Control Board (CPCB), Delhi.
We first missing values in the whole data set were completed by using the mean of the corresponding series.
| SUMMARY OUTPUT | ||||||
| Regression Statistics | ||||||
| Multiple R | 0.779421 | |||||
| R Square | 0.607498 | |||||
| Adjusted R Square | 0.606888 | |||||
| Standard Error | 48.52492 | |||||
| Observations | 646 | |||||
| ANOVA | ||||||
| df | SS | MS | F | Significance F | ||
| Regression | 1 | 2347025 | 2347025 | 996.7541 | 6.6E-133 | |
| Residual | 644 | 1516406 | 2354.668 | |||
| Total | 645 | 3863431 | ||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
| Intercept | 8.022893 | 5.343874 | 1.501325 | 0.133762 | -2.47063 | 18.51641 |
| PM10 | 1.072772 | 0.033979 | 31.57141 | 6.6E-133 | 1.006048 | 1.139495 |
The result shows that 60% variation is explained by the independent variable. There is a positive relationship exist in these variables.
| SUMMARY OUTPUT | ||||||
| Regression Statistics | ||||||
| Multiple R | 0.94475 | |||||
| R Square | 0.892552 | |||||
| Adjusted R Square | 0.892385 | |||||
| Standard Error | 25.38887 | |||||
| Observations | 646 | |||||
| ANOVA | ||||||
| df | SS | MS | F | Significance F | ||
| Regression | 1 | 3448312 | 3448312 | 5349.581 | 0 | |
| Residual | 644 | 415119.1 | 644.5948 | |||
| Total | 645 | 3863431 | ||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
| Intercept | 11.36439 | 2.333399 | 4.870316 | 1.4E-06 | 6.782401 | 15.94638 |
| X Variable 1 | 2.057698 | 0.028133 | 73.14083 | 0 | 2.002454 | 2.112942 |
The result shows that 89% variation is explained by the independent
variable. There is a strong positive relationship exist in these
variables.
milcah answered 8 months agoRelated Solutions
As a researcher, you will be considering the relationships between variables regularly. Linear correlation is the...
As a researcher, you will be considering the relationships
between variables regularly. Linear correlation is the most basic
relationship that may exist between two variables. This assignment
will you give the opportunity to see how statistics can start to
answer the research questions you will be faced with in your field
of study.
Correlation Project Directions:
Consider a possible linear relationship between two variables
that you would like to explore.
Define the relationship of interest and a data collection
technique....
Regression and correlation analysis both describe the strength of linear relationships between variables. Consider the concepts...
Regression and
correlation analysis both describe the strength of linear
relationships between variables. Consider the concepts of education
and income. Many people would say these two variables are related
in a linear fashion. As education increases, income usually
increases (although not necessarily at the same rate). Can you
think of two variables that are related in such a way that their
relationship changes over their range of possible values (i.e., in
a curvilinear fashion)? How would you analyze the relationship...
You wish to determine if there is a linear correlation between the two variables at a...
You wish to determine if there is a linear correlation between
the two variables at a significance level of α=0.10α=0.10. You have
the following bivariate data set.
x
y
85.9
65.4
73.2
49.4
62.2
36.9
86.4
52.3
76
52.8
70.8
34
77.6
59.4
70.1
47.2
80.2
65.8
83.9
46.2
80.1
47
68.8
50.8
85.5
82.9
74.3
69.9
72.7
42.8
87.1
65.6
70.4
59.3
85.2
64.5
63.3
31.9
92.6
80.4
87
62.2
77.3
63.8
93.9
64.4
What is the correlation coefficient...
You wish to determine if there is a linear correlation between the two variables at a...
You wish to determine if there is a linear correlation between
the two variables at a significance level of α=0.005α=0.005. You
have the following bivariate data set.
x
y
39
52.7
29.7
82.5
32.1
72.4
39.4
98.3
31.1
51.4
43.1
51.8
35.5
43.8
29.5
90.8
38.4
100
36.8
7.4
34
67.5
28.3
97.2
32.2
82.2
29.9
28.9
What is the correlation coefficient for this data set?
r =
What is the p-value for this correlation coefficient?
p-value =
Your final...
You wish to determine if there is a linear correlation between the two variables at a...
You wish to determine if there is a linear correlation between
the two variables at a significance level of α=0.01. You have the
following bivariate data set.
x
y
30.1
49.7
47.3
53.8
55.7
49.6
35.7
58.9
42.7
53.7
36.4
56.8
42.6
62.9
34
61.1
47.5
65
57.3
47
34.5
63.3
62.6
55.2
What is the correlation coefficient for this data set?
r =
To find the p-value for a correlation coefficient, you need to
convert to a t-score:
t=√r2(n−2)1−r2...
You wish to determine if there is a linear correlation between the two variables at a...
You wish to determine if there is a linear correlation between
the two variables at a significance level of α=0.10. You have the
following bivariate data set.
x
y
30.5
114.8
40.9
130.6
25.9
19.8
25.1
23.9
27.9
96.4
40.8
91.6
32.4
41.1
27.6
34
38.3
145.8
32.8
138.8
32.5
95.5
37.4
120.4
22
84.6
41
65.6
30.8
27.4
21.8
102
33
66.4
31.9
59.8
27.8
41.4
30.1
85.8
26.2
71.7
28.5
35.1
26.9
67.6
1. What is the correlation...
You wish to determine if there is a linear correlation between the two variables at a...
You wish to determine if there is a linear correlation between
the two variables at a significance level of α=0.005α=0.005. You
have the following bivariate data set.
x
y
13.6
126.6
33.5
42.2
17.6
78.5
39
32.7
33
61.5
47.1
25.1
41.4
34.7
74
-41
68.7
-3
41.2
59.9
27.1
89.2
27.2
78.7
-19.8
179.9
62.7
-1.1
21
112.8
40.6
32.6
27.3
63.2
27.6
59.6
31.4
52.7
56.6
9.1
55
28.6
40.5
46.3
17.9
91.8
52.1
-6.6
38
21.3
24.5...
You wish to determine if there is a linear correlation between the two variables at a...
You wish to determine if there is a linear correlation between
the two variables at a significance level of α=0.005α=0.005. You
have the following bivariate data set.
x
y
101.8
97.3
72.4
18.1
94.1
94.4
43.8
-23.5
84.5
84.5
68.1
27.2
51.3
3.9
88.6
87.8
77
53.1
56.9
13.7
72.7
29.5
74.1
36.7
112.3
112.7
70.9
40.1
What is the correlation coefficient for this data set?
r =
(report answer accurate to at least 3 decimal places)
To find the...
You wish to determine if there is a linear correlation between the two variables at a...
You wish to determine if there is a linear correlation between
the two variables at a significance level of α=0.01. You have the
following bivariate data set.
x
y
75
22.4
50.4
41.3
94.4
27.3
60.1
35
63.9
32.2
43.8
52.1
59
42.2
54.5
35.9
75.8
19.2
49.4
46.4
42.5
59.4
29.7
59.3
65.2
27.9
56.6
31.2
38.6
48.3
50.7
32.9
60
35.1
61
35.6
59.2
32.7
94.4
11.8
42.3
47.5
71.1
19.3
65.9
42.2
17.3
65.3
What is the...
You wish to determine if there is a linear correlation between the two variables at a...
You wish to determine if there is a linear correlation between
the two variables at a significance level of α=0.01α=0.01. You have
the following bivariate data set.
x
y
53.8
140.7
59.6
106.5
91.7
8.3
85.5
23
93.1
42.2
77.7
48.3
71.4
86.7
69.5
85.1
80.9
59.1
62.5
112.7
79.6
103
76.6
69
76.1
32.1
What is the critival value for this hypothesis test?
rc.v. =
What is the correlation coefficient for this data set?
r =
Your final conclusion...
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