Univariate analysis using simple linear regression Conduct a univariate analysis
ID: 3226087 • Letter: U
Question
Univariate analysis using simple linear regression
Conduct a univariate analysis to test the hypothesis that exposure to stress at work might lead to an increase in body weight in kilograms (Tip: click analyze, select regression, choose linear, enter “is work stressful” into the independent variable box and “weight” into the dependent variable box). Include the SPSS Model Summary table and answer the following questions:
Model Summary
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.081a
.007
.005
12.3517
a. Predictors: (Constant), is work stressful
ANOVAa
Model
Sum of Squares
df
Mean Square
F
Sig.
1
Regression
745.135
1
745.135
4.884
.027b
Residual
111829.214
733
152.564
Total
112574.348
734
a. Dependent Variable: weight in kgs
b. Predictors: (Constant), is work stressful
Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
B
Std. Error
Beta
1
(Constant)
66.204
.784
84.483
.000
is work stressful
1.168
.528
.081
2.210
.027
a. Dependent Variable: weight in kgs
Univariate analysis using simple linear regression – Model Summary Table
The Model Summary table (Insert the table here)
What does the R value represent? Interpret the R value.
What does the R Square value represent? Interpret the R Square value.
What are your conclusions based on the Model Summary table?
Univariate analysis using simple linear regression – Anova Table
The Anova table (Insert the table here)
What is the F-ratio? Interpret the value of the F-ratio.
Interpret the significance value for the F-ratio.
What are your conclusions based on the Anova table?
Univariate analysis using simple linear regression – Coefficient Table
The Coefficients Table (Insert the Coefficients table here)
What is the beta-coefficient for the intercept in this model?
What is the beta coefficient for work stress?
Interpret the beta coefficient for work stress in relation to body weight.
Interpret the significance value for the beta coefficient for work stress.
Interpret the confidence interval for the beta coefficient for work stress.
Using the Regression Model
By substituting the values from the Coefficients table into the regression equation we can work out the predicted weight for given levels of work stress. For example:
Weight = 0 + 1Stress
= 66.204 + (1.168 x stress)
Work stress is represented by a four category variable (see categories below):
0 = never find the work stressful
1 = occasionally find the work stressful
2 = find work stressful about half the time 3 = find work stressful all the time
What is the predicted value of weight in kilograms for employees who find their work stressful “half the time”
What is the predicted value of weight in kilograms for employees who find their work stressful “always”
Model Summary
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.081a
.007
.005
12.3517
a. Predictors: (Constant), is work stressful
Explanation / Answer
What does the R value represent? Interpret the R value.
Answer: R value is the multiple correlation coefficient of dependent variable with all the predictors. So, multiple correlation between weight and work stressful is 0.081
What does the R Square value represent? Interpret the R Square value.
R-sqaures tells us that work stressful explained 0.7% of the variability in weight
What are your conclusions based on the Model Summary table?
From model summary table we observe that model is not a good fit as low values of R-sqaures
Univariate analysis using simple linear regression – Anova Table
The Anova table (Insert the table here)
What is the F-ratio? Interpret the value of the F-ratio.
F-ratio is the test statistic used to test the joint significance of all the coefficients of all predictors. Here F ratio is 4.884 with p=0.027<0.05, so coefficient of work stressful is significant at 5% level
Interpret the significance value for the F-ratio.
p-valu=0.027 which means coefficient of work stressful is significant at 5% level
What are your conclusions based on the Anova table?
The coefficient of work stressful is significant at 5% level
Univariate analysis using simple linear regression – Coefficient Table
The Coefficients Table (Insert the Coefficients table here)
What is the beta-coefficient for the intercept in this model?
Intercept=66.204
What is the beta coefficient for work stress?
Slope=1.168
Interpret the beta coefficient for work stress in relation to body weight.
Corresponding to a unit increase in work stress there is on an average an increase of 1.168 kg in weight, holding other things constant
Interpret the significance value for the beta coefficient for work stress.
p-value=0.027<0.05, so coefficient of work stress is significant.
Interpret the confidence interval for the beta coefficient for work stress.
Degree of freedom=733, critical t0.05(733)=1.96
So 95% confidence interval =1.168-1.96*0.528, 1.168+1.96*0.528
=(0.13312 2.20288)
This interval is 95% confident to contain the true population value of slope
Using the Regression Model
By substituting the values from the Coefficients table into the regression equation we can work out the predicted weight for given levels of work stress. For example:
Weight = 0 + 1Stress
= 66.204 + (1.168 x stress)
Work stress is represented by a four category variable (see categories below):
0 = never find the work stressful
1 = occasionally find the work stressful
2 = find work stressful about half the time 3 = find work stressful all the time
What is the predicted value of weight in kilograms for employees who find their work stressful “half the time”
Predicted value=66.204+1.168*2=68.54kg
What is the predicted value of weight in kilograms for employees who find their work stressful “always”
Predicted value=66.204+1.168*3= 69.708kg
What does the R value represent? Interpret the R value.
Answer: R value is the multiple correlation coefficient of dependent variable with all the predictors. So, multiple correlation between weight and work stressful is 0.081
What does the R Square value represent? Interpret the R Square value.
R-sqaures tells us that work stressful explained 0.7% of the variability in weight
What are your conclusions based on the Model Summary table?
From model summary table we observe that model is not a good fit as low values of R-sqaures
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