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# Correlation and Simple Linear Regression

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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?

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
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

https://brainmass.com/statistics/regression-analysis/correlation-simple-linear-regression-15219

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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
Standard Error 5.089839735
Observations 7

R Square = 0.914411327

Therefore r= correlation coefficient=√ R Square= √0.914411327 =0.956248

2.) What is the value of the coefficient of determination?

Regression Statistics

Multiple R 0.95624857
R Square 0.914411327
Standard Error 5.089839735
Observations 7

coefficient of determination= R Square = 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 0.79659 7.30883 0.00075

4.) What is the value of the slope 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 0.79659 7.30883 0.00075

5.) Write the equation of the least squares line for this set of data.

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

Y=-3.88811 + 5.81993 X

6.) Is the slope of the line significant (yes or no):

a.) at p < .05?
b.) at p < .01?
c.) at p < .001?

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

p value=0.00075

a.) at p < .05? p = .05 >0.00075 hence significant
b.) at p < .01? p = .01 >0.00075 hence significant
c.) at p < .001? p = .001 >0.00075 hence significant

7.) Based on these results, write a sentence explaining the relationship between the dependent and independent variable.

For a unit change in the dependent variable X the dependent variable Y changes by 5.81993 (slope of regression line)

8.) Compute predicted y for x = 10 using the equation of the least squares line for this data set.

Y=-3.88811 + 5.81993 X

X= 10

Therefore Y= -3.88811 + 5.81993 X = -3.88811 + 5.81993 * 10= -3.88811 + 58.1993 = 54.31119

9.) What percent of the variation in y (dependent variable) is explain by x (independent) variable?

Regression Statistics

Multiple R 0.95624857
R Square 0.914411327
Standard Error 5.089839735
Observations 7

R Square 0.914411327

percent of the variation in y (dependent variable) is explain by x (independent) variable= 91.44% ( R square value expressed as a percentage)

10.) What value represents the strength of the relationship between the independent and dependent variable?

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

F value and Significance F
F value is very high=53.4189
Corresponding to this value of F, Significance F =0.00075 Which means that the relationship is significant at level=0.00075 or 0.075%
This means that the strength of the relationship between the independent and dependent variable is very high ( the lower the level of significance the higher the strength of relationship)

In simple linear regression, how many independent variables may be used?

Any number

How many dependent variables may be used?
One

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.95624857
R Square 0.914411327
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

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!