(a)
To explain:
The
(a)
Explanation of Solution
Given:
The table of the exposure and change.
Concept used:
Formula
The binomial distribution
Calculation:
Scatter plot is given as the table
The weak is negative relationship exists.
Because the value of
Where
Let us perform the regression
Regressing sub concussion exposure on white matter change with below mentioned steps in excel
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
Draw the table
Degree | SS | MS | F | Significant | |
Regression | |||||
Residual | |||||
Total |
Draw the second table
Coefficient | Standard Error | t Stat | P-value | Lower | Upper | Lower | Upper | |
Intercept | ||||||||
(b)
To find:
Theregression standard error of the given data.
(b)
Explanation of Solution
Given:
The table of the exposure and change.
Concept used:
Formula
The binomial distribution
Calculation:
Scatter plot is given as the table
The weak is negative relationship exists.
Because the value of
Where
Let us perform the regression
Regressing sub concussion exposure on white matter change with below mentioned steps in excel
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
Draw the table
Degree | SS | MS | F | Significant | |
Regression | |||||
Residual | |||||
Total |
Draw the second table
Coefficient | Standard Error | t Stat | P-value | Lower | Upper | Lower | Upper | |
Intercept | ||||||||
Here
So least squares regression line
Change (
Regression standard error
The low p-value of
Hence, the null hypothesis of no relationship between exposure and white matter change can be rejected in favor of the alternative hypothesis at a confidence level of
(c)
To explain:
Theequation for the least-squares regression line without data point and test null hypothesis of the given data.
(c)
Explanation of Solution
Given:
The table of the exposure and change.
Concept used:
Formula
The binomial distribution
Calculation:
Scatter plot is given as the table
The weak is negative relationship exists.
Because the value of
Where
Let us perform the regression
Regressing sub concussion exposure on white matter change with below mentioned steps in excel
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
Draw the table
Degree | SS | MS | F | Significant | |
Regression | |||||
Residual | |||||
Total |
Draw the second table
Coefficient | Standard Error | t Stat | P-value | Lower | Upper | Lower | Upper | |
Intercept | ||||||||
Here
So least squares regression line
Change (
Regression standard error
The low p-value of
Hence, the null hypothesis of no relationship between exposure and white matter change can be rejected in favor of the alternative hypothesis at a confidence level of
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
Draw the table
Degree | SS | MS | F | Significant | |
Regression | |||||
Residual | |||||
Total |
Draw the second table
Coefficient | Standard Error | t Stat | P-value | Lower | Upper | Lower | Upper | |
Intercept | ||||||||
Standard error is same
But the p value is
Exposure is not good predictor of Change in white matter.
Also, the Exposure coefficient has come down from
(d)
To explain:
Theimpact of the usual observation on the
(d)
Explanation of Solution
Given:
The table of the exposure and change.
Concept used:
Formula
The binomial distribution
Calculation:
Scatter plot is given as the table
The weak is negative relationship exists.
Because the value of
Where
Let us perform the regression
Regressing sub concussion exposure on white matter change with below mentioned steps in excel
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
Draw the table
Degree | SS | MS | F | Significant | |
Regression | |||||
Residual | |||||
Total |
Draw the second table
Coefficient | Standard Error | t Stat | P-value | Lower | Upper | Lower | Upper | |
Intercept | ||||||||
Here
So least squares regression line
Change (
Regression standard error
The low p-value of
Hence, the null hypothesis of no relationship between exposure and white matter change can be rejected in favor of the alternative hypothesis at a confidence level of
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
Draw the table
Degree | SS | MS | F | Significant | |
Regression | |||||
Residual | |||||
Total |
Draw the second table
Coefficient | Standard Error | t Stat | P-value | Lower | Upper | Lower | Upper | |
Intercept | ||||||||
Standard error is same
But the p value is
Exposure is not good predictor of Change in white matter.
Also, the Exposure coefficient has come down from
The Change in white matter will not actually change as fast
So,eliminate of the outlier data points.
The Outlier data points tend to increase the correlation between the two variables.
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Chapter 23 Solutions
Practice of Statistics in the Life Sciences
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