Answer:
We can not state the exact probability that y will fall between 195 and 205
Step-by-step explanation:
* Lets explain how to solve the problem
- Regression model applies with f(30) = 100 and f(31) = 20
- The variance = 25
- An observation on y will be made for x = 5
- Suppose that the regression model is
[tex]y=B_{0}+B_{1}x[/tex]
∵ [tex]B_{0}=100[/tex]
∵ [tex]B_{1}=20[/tex]
∵ x = 5
∴ Y = 100 + 20(5) = 100 + 100 = 200
∴ Y = 200
- But the regression model is without error term [tex]e_{i}[/tex]
∵ We do not know the probability distribution of y for each value
of x we only know the value of y at one value of x
∵ We know that the mean of distribution is 100 + 20x
∵ We know the variance of distribution is 25
∵ We don not know the shape of the distribution
- We can not find the exact value of probability of y without the
Normal error [tex]e_{i}[/tex] and the regression model must be
[tex]y=B_{0}+B_{1}x+e_{i}[/tex] to know that it has a normal distribution
∴ We can not calculate the exact value of probability of y
∴ We can not state the exact probability that y will fall between 195
and 205
The exact probability that y will fall between 195 and 205 is we can not state the exact probability because the calculated value is 200, where 200 is five less than 205 and five more than 195
Regression analysis is the set of statistical processes to estimate the relationships between the dependent variable and one or more independent variables.
The probability we computed is called exact probability, exact itself means the probabilities that calculated exactly
In a simulation exercise, regression model [tex](1.1)[/tex] applies with [tex]f_{30} = 100, f_{31} = 20,[/tex] and [tex]a^2 = 25[/tex]. an observation on [tex]y[/tex] will be made for [tex]x = 5.[/tex]
Normal error regression model is stated as follows:
[tex]Y_1 = f_{30} + f_{31}*x[/tex]
[tex]Y_1 = 100 + 20*5[/tex]
[tex]Y_1 = 100 + 100[/tex]
[tex]Y_1 = 200[/tex]
No, we cannot state the exact probability that Y will fall between 195 and 205. It is because the calculated value is 200, where 200 is five less than 205 and five more than 195
Grade: 5
Subject: Math
Chapter: regression model
Keywords: probability, simulation exercise, exact, regression model, model
