select at least three variables that you believe have a linear relationship spec
ID: 3220723 • Letter: S
Question
select at least three variables that you believe have a linear relationship specify which variable is dependent and which are independent collected data for these variables and describe your data collection techniques and why it was appropriate as well as why the sample size data submit the data collected by submitting the SPSS data file with your submission find the correlation coefficient see each of the possible. Of dependent and independent variables in describe the relationship in terms of strength and direction find a linear model of the relationship between the three variables of Interest explain the validity of the model
Explanation / Answer
Solution:
Here, we have to select the three variables which have a linear relationship. For this multiple regression study we select the three linearly related variables as GPA of the student, number of TV hours in a week and academic year of the student.
For this regression analysis, the dependent variable or response variable is given as GPA of the student while independent variables or predictors are selected as number of TV hours in a week and academic year of the student. We have to find the regression equation for the prediction of the GPA of the student based on the number of hours of TV and academic year of student. We use the simple random sampling method for the collection of the data. We randomly select the data for 40 students from the school record. We choose the sample size as 40. We know that if the sample size is too small, it results in the biased estimates and the regression equation based on data with small sample size is not helpful for further estimation.
The descriptive statistics for the given variables are summarised as below:
Descriptive Statistics
Mean
Std. Deviation
N
GPA
3.0983
.44556
40
Hours TV
15.3000
7.16902
40
Year
2.4000
1.12774
40
The correlation coefficients between the pairs of variables are given as below:
Correlations
GPA
Hours_TV
Year
Pearson Correlation
GPA
1.000
-.772
.573
Hours TV
-.772
1.000
-.650
Year
.573
-.650
1.000
Sig. (1-tailed)
GPA
.
.000
.000
Hours TV
.000
.
.000
Year
.000
.000
.
N
GPA
40
40
40
Hours TV
40
40
40
Year
40
40
40
From the above table, it is observed that there is a strong negative linear relationship exists between the GPA and number of TV hours while there is a considerable positive linear relationship exists between the GPA and academic year of the student. There is a considerable negative correlation exists between the number of TV hours and year of the student. The regression analysis is given as below:
Model Summary
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.778a
.605
.584
.28753
a. Predictors: (Constant), Year, Hours TV
The multiple correlation coefficient is given as 0.778 which means there is a strong positive association between the dependent and independent variables. The value of the R square or the coefficient of determination is given as 0.605 which means about 60.5% of the variation in the dependent variable GPA is explained by the independent variables TV hours and year. The ANOVA table for this regression is given as below:
ANOVA
Model
Sum of Squares
df
Mean Square
F
Sig.
1
Regression
4.683
2
2.342
28.325
.000a
Residual
3.059
37
.083
Total
7.742
39
a. Predictors: (Constant), Year, Hours TV
b. Dependent Variable: GPA
The p-value for this regression equation is given as 0.00 which is less than the level of significance or alpha value 0.05, so we reject the null hypothesis that the given regression model is not statistically significant. This means we conclude that there is sufficient evidence that there is a significant relationship or association exists between the dependent variable GPA and independent variables TV hours and year of the student. The given regression model is valid for the future use for the prediction of the GPA of the student based on the TV hours and academic year of the student. The regression coefficients for the regression equation are summarized as below:
Coefficients
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
B
Std. Error
Beta
1
(Constant)
3.639
.239
15.240
.000
Hours TV
-.043
.008
-.692
-5.090
.000
Year
.049
.054
.124
.910
.369
a. Dependent Variable: GPA
The regression equation for the prediction of GPA is given as below:
GPA = 3.639 – 0.043*TV hours + 0.049*Year
By using this regression we can predict the value for GPA of the student based on the TV hours and year of the student.
Appendix:
Data:
GPA
Hours TV
Year
3.29
2
4
2.65
24
3
1.94
27
1
3.39
8
2
3.59
13
4
3.42
14
2
3.22
6
2
3.45
11
3
3.57
15
2
3.42
7
2
2.88
20
1
3.38
13
2
3.04
20
2
3.08
20
1
3.32
13
2
2.26
25
1
3.13
19
1
3.62
9
4
3.19
15
3
2.23
25
1
3.44
13
3
3.32
4
4
3.07
18
3
3.27
14
2
3.47
15
4
2.4
24
1
3.36
17
3
3.35
4
4
2.25
26
3
2.93
20
1
2.79
22
1
3.63
10
2
2.49
22
1
3.29
2
4
3.4
3
4
3.44
12
4
3.51
16
3
3.12
20
2
2.9
20
3
2.43
24
1
Descriptive Statistics
Mean
Std. Deviation
N
GPA
3.0983
.44556
40
Hours TV
15.3000
7.16902
40
Year
2.4000
1.12774
40
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