A sample of 15 countries was surveyed in order to examine the relationship between the Infant Mortality rate (Y), the Literacy rate (X1), the Population Density (X2), the N. of Inhabitants Per Physician (X3), and Income per Capita (X4). The data collected were summarized with the following statistics.
Variable | | S | b | Y X1 X2 X3 X4 | 48.3681.0588.472062.2712000.00 | 23.6823.48141.852009.256000.00 | --------1.05.05.002-.003 |
1. Find the simple regression equation for the relationship between Y & X1, and explain its meaning as well as the meaning of its slope and constant. What would you predict for X1=70% ?
Simple regression equation:
This equation is used for two purposes: * Explain the variation in Y using X1 * Predict Y knowing X1
The constant a=133.46 means that if X1=0% literacy rate, then Y=133.46 number of infant deaths per 1000 live births.
The slope b=-1.05 means that if X1 increases by 1% literacy rate, Y would decrease by 1.05 infant deaths per 1000 live births.
For prediction: Y=133.46-1.0570=59.96 infant deaths per 1000 live births.
If the population>15yrs who read and write is 70% then the number of infant deaths per 1000 live births is 59.96.
2. Find the multiple regression equation. Interpret its meaning and the meaning of its slopes and constant.
Multiple Regression Equation (MRE):
The constant a=Y-[b1X1+b2X2+b3X3+b4X4] a= 48.37-[-1.05(81.05)+0.05(88.47)+0.002(2062.27)- 0.003(12000.00)]= a= 48.37-(-112.55)=160.92
This equation has two purposes: * Explain the variation in Y using all four X’s * Predict Y knowing all four X’s
The constant a=160.92, means that if all X’s=0, then Y=160.92 infant deaths per 1000 live births.
The partial slopes
Partial slope b1=-1.05, if X1