Statistics Problems Assignment (pdf)

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Statistics Problems
Student Name: Student ID:
Due Date: Unit Name:

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Answer 1
(a) ANS: The Pearson correlation was calculated in SPSS using two variables FVC and
HEIGHT. Mean FVC and HEIGHT were 3.07 (SD = 0.89) and 1.65 (SD = 0.08) (Table
1). Total 1180 observations were explored. The Pearson correlation was calculated as
0.695 (Table 2).
Table 1: Descriptive Statistics
Mean Std. Deviation N
FVC 3.0666 .89235 1180
HEIGHT 1.6457 .08663 1180
Table 2: Correlations for FVC and HEIGHT
FVC HEIGHT
FVC
Pearson Correlation 1 .695
Sig. (2-tailed) .000
Sum of Squares and Cross-
products 938.824 63.354
Covariance .796 .054
N 1180 1180
HEIGHT
Pearson Correlation .695 1
Sig. (2-tailed) .000
Sum of Squares and Cross-
products 63.354 8.848
Covariance .054 .008
N 1180 1180

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95% confidence interval for this correlation
Fisher’s Z transform method was used to calculate the confidence intervals. The value of Z
was calculated using the formula
Z ( prime )=0. 5 *ln ( 1+r
1−r )
The standard error for the method is
1
√ N −3 where N is the number of pair of observations.
Here correlation coefficient is r=0. 6 , sample size is N=1180 and S . E=0 . 03 , value
of standard normal variable is Z =1.96 for 95% confidence interval (Puth, Neuhäuser &
Ruxton, 2015).
So the value of Z (prime) is 0.69 for r=0. 6 using the formula
Z ( prime )=0. 5 *ln ( 1+r
1−r )
So the lower limit for confidence interval is 0.69 - (1.96)*(0.03) = 0.6312.
The upper limit for confidence interval is 0.69 + (1.96)*(0.03) = 0.7488
Hence the 95% confidence interval for this correlation is [0.63, 0.75].

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(b) (i)SPSS software package was used to find the linear regression model of FVC on
Height. The model was able to explain 48.3% variance of the dependent FVC variable.
The F value of the model was 1101.34 with p value less than 0.05. This indicated the fact
that the model was highly significant and FVC was significantly dependent on Height
(Goh, Hall, & Rosenthal, 2016)
Table 3: R-square summary
Model R R Square Adjusted R
Square
Std. Error of the
Estimate
1 .695a .483 .483 .64178
a. Predictors: (Constant), HEIGHT
b. Dependent Variable: FVC
Table 4: ANOVA table for regression model
Model Sum of Squares df Mean Square F Sig.
1
Regression 453.624 1 453.624 1101.339 .000b
Residual 485.200 1178 .412
Total 938.824 1179
The regression model equation was Y = 7 .16 X−8 . 72 where Y was FVC and X was
Height (Seber & Lee, 2012). The slope was negative which signified that hypothetically
FVC would become negative for zero Height in the described model. The significance
value of the independent variable as well as the constant was less than 0.05, and
association of the variables was significant. The 95% CI and PI for each subject has been
provided in table 15 (Appendix).
Table 5: Regression model
Model Un-standardized Coefficients Standardized
Coefficients
t Sig.