Homework SourseProblem 2Regression Use STATE10HEALTH50 to perform a regress
Problem 2-Regression
Use STATE10-HEALTH-50 to perform a regression analysis.
On the SPSS menu, follow this command: Analyze à Regression àLinear
Perform a regression analysis between IMR (dependent) and low weight birth (independent). Fill the following blanks
What is the Constant “a”?: 0.509
What is the slope, the Regression coefficient (unstandardized) b? 0.790
What is the p value?: 0.000 Is it significant? Yes [ ] No [ ]
What is R and R2in this analysis?: R 0.777, R2: 0.604
In your own words, describe the relationship between IMR and low weight birth variables. What does R2tell us? The independent variable (low weight birth) affects the infant mortality rate. R2tells us that it effected by 0.604 or 60.4%.
Perform a multivariate regression to examine the influence of three independent variables environment (Toxic release), mother’s age (births to teenage mothers) and median household income. Use the Coefficient Table and plug in the table data into the following formula
Y = a + b1 X1 + b2 X2 + b3 X3
Where:
a =constant
X1 = toxic release b1 = beta for toxic release
X2 = Births to teenage b2= beta for Birth to teen
X3 = Median income b3 = Median income
Interpret the formula
Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
B
Std. Error
Beta
1
(Constant)
5.595
2.264
2.471
.017
Toxic Releases: Total Pollution Released: 2007
1.807E-9
.000
.132
1.156
.254
Births to Teenage Mothers as Percent of All Births: 2009
.262
.091
.507
2.871
.006
Median Household Income: 2008
-2.910E-5
.000
-.170
-.986
.329
a. Dependent Variable: Infant Mortality Rate per 1,000 Live Births: 2006
Interpret the formula
Which variable is the strongest predictor of the dependent IMR variable? ------------------ ?
Which variable is the weakest one? ---------------------
Altogether, what percentage of change in IMR is explained by the independent variables?
| Coefficientsa | ||||||
| Model | Unstandardized Coefficients | Standardized Coefficients | t | Sig. | ||
| B | Std. Error | Beta | ||||
| 1 | (Constant) | 5.595 | 2.264 | 2.471 | .017 | |
| Toxic Releases: Total Pollution Released: 2007 | 1.807E-9 | .000 | .132 | 1.156 | .254 | |
| Births to Teenage Mothers as Percent of All Births: 2009 | .262 | .091 | .507 | 2.871 | .006 | |
| Median Household Income: 2008 | -2.910E-5 | .000 | -.170 | -.986 | .329 | |
| a. Dependent Variable: Infant Mortality Rate per 1,000 Live Births: 2006 |
Solution
We are given that, dependent variable Y is IMR.
and independent variable X is low weight birth.
Constant (a) = 0.509
regression coefficient (slope or b) = 0.790
The regression equation is,
Y = 0.509 + 0.790*X
Here positive slope indicates that there is positive relationship between IMR and low weight birth.
correlation coefficient (r) = 0.777
R-square is (R2) = (0.777)^2 = 0.604
What is the p value?: 0.000 Is it significant? Yes [ ] No [ ]
What is R and R2 in this analysis?: R 0.777, R2: 0.604
R2 interpretation :
It expresses the proportion of the variation in IMR which is explained by variation in lowe weight birth.
P-value = 0.000
It indicates that it is significant that is reject H0.
Perform a multivariate regression to examine the influence of three independent variables environment (Toxic release), mother’s age (births to teenage mothers) and median household income. Use the Coefficient Table and plug in the table data into the following formula
Y = a + b1 X1 + b2 X2 + b3 X3
Where:
a =constant
X1 = toxic release b1 = beta for toxic release
X2 = Births to teenage b2= beta for Birth to teen
X3 = Median income b3 = Median income
By using table,
constant (a) = 5.595
b1 = beta for toxic release = 1.807E-9
b2 = beta for Birth to teen = 0.262
b3 = Median income = -2.910E-5
Plug all the values of constant and coefficients,
Y = 5.595 + 1.807E-9*X1 + 0.262*X2 - 2.910E-5*X3
Dependent Variable: Infant Mortality Rate per 1,000 Live Births: 2006
The variable which has smallest P-value that variable is strongest predictor of the dependent IMR variable.
Assume alpha (level of significance) = 0.05
We have see in the table the P-value for Births to teenage is 0.006 which is less than alpha.
Births to teenage is significant variable and strongest predictor of the dependent IMR variable.
That is variable births of teenage is include for the further analysis.
The variable which has P-value greator than alpha that variable is weakest predictor of the dependent IMR variable.
Here P-value for toxic release is 0.254 and for Median income is 0.329.
Both the P-values are greator than alpha.
Fail to reject null hypothesis at 0.05 level of significane.
Both the variables toxic release and median income are insignificant variable hence they are weakest one.
These two variables are excluded from the further analysis.
