Correlation and Simple Linear Regression
Using the Excel SUMMARY OUTPUT below, complete the following:
All calculations accurate to four decimal places
1.) What is the value of the correlation coefficient?
2.) What is the value of the coefficient of determination?
3.) What is the value of the y-intercept of the least squares line?
4.) What is the value of the slope of the least squares line?
5.) Write the equation of the least squares line for this set of data.
6.) Is the slope of the line significant (yes or no):
a.) at p < .05?
b.) at p < .01?
c.) at p < .001?
7.) Based on these results, write a sentence explaining the relationship between the dependent and independent variable.
8.) Compute predicted y for x = 10 using the equation of the least squares line for this data set.
9.) What percent of the variation in y (dependent variable) is explained by x (independent) variable?
10.) What value represents the strength of the relationship between the independent and dependent variable?
In simple linear regression, how many independent variables may be used?
How many dependent variables may be used?
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.95624857
R Square 0.914411327
Adjusted R Square 0.897293593
Standard Error 5.089839735
Observations 7
ANOVA
df SS MS F Significance F
Regression 1 1383.8962 1383.8962 53.4189 0.00075
Residual 5 129.53234 25.906469
Total 6
Coefficients Standard Error t Stat P-value
Intercept -3.88811 4.23842 -0.91751 0.40096
X Variable 1 5.81993 0.79659 7.30883 0.00075
please see the attached file
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Using the Excel SUMMARY OUTPUT below, complete the following:
All calculations accurate to four decimal places
1.) What is the value of the correlation coefficient?
Regression Statistics
Multiple R 0.95624857
R Square 0.914411327
Adjusted R Square 0.897293593
Standard Error 5.089839735
Observations 7
R Square = 0.914411327
Therefore r= correlation coefficient=√ R Square= √0.914411327 =0.956248
Answer: r= correlation coefficient=0.956248
2.) What is the value of the coefficient of determination?
Regression Statistics
Multiple R 0.95624857
R Square 0.914411327
Adjusted R Square 0.897293593
Standard Error 5.089839735
Observations 7
coefficient of determination= R Square = 0.914411327
Answer: 0.914411327
3.) What is the value of the y-intercept of the least squares line?
Coefficients Standard Error t Stat P-value
Intercept -3.88811 4.23842 -0.91751 0.40096
X Variable 1 5.81993 ...
Solution Summary
Using Excel output questions on correlation and regression have been answered. The value of the coefficients of determinations are analyzed.