Respuesta :
Answer:
The regression equation for the winter rainy days is "Humidity = (β0 + β5) + β1Temperature".
Step-by-step explanation:
Given:
Humidity = β0 + β1Temperature + β2Spring + β3Summer + β4Fall + β5Rain + ε ...........(1)
Since there can be only one of spring, summer,fall, and winter at a point in time or in a season, we will have the following when there are winter rainy days:
Spring = 0
Summer = 0
Fall = 0
Rain = 1
Substituting all the relevant values into equation (1) and equating ε also to 0, a reduced form of equation (1) can be obtained as follows:
Humidity = β0 + β1Temperature + (β2 * 0) + (β3 * 0) + (β4 * 0) + (β5 * 1) + 0
Humidity = β0 + β1Temperature + 0 + 0 + 0 + β5 + 0
Humidity = (β0 + β5) + β1Temperature
Therefore, the regression equation for the winter rainy days is "Humidity = (β0 + β5) + β1Temperature".
The regression equation for winter rainy days is
Humidity = β0 + β5 + β1Temperature
The regression model is given as:
Humidity = β0 + β1Temperature + β2Spring + β3Summer + β4Fall + β5Rain + ε
To determine the regression equation for winter rainy days, we consider that:
[tex]Rain = 1[/tex]
This also means that:
[tex]Spring = 0[/tex]
[tex]Summer = 0[/tex]
[tex]Fall = 0[/tex]
ε = 0
Because each of these seasons can only happen one at a time, and the current season is winter
So, the regression equation becomes
Humidity = β0 + β1Temperature + (β2 * 0) + (β3 * 0) + (β4 * 0) + (β5 * 1) + 0
Evaluate the products
Humidity = β0 + β1Temperature + 0 + 0 + 0 + β5 + 0
The sum of 0 is 0. So, we have:
Humidity = β0 + β1Temperature + β5
Rewrite as:
Humidity = β0 + β5 + β1Temperature
Hence, the regression equation for winter rainy days is
Humidity = β0 + β5 + β1Temperature
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