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[answered] A simple linear regression model has been developed and an


A simple linear regression model has been developed and an F test is going to be conducted to determine whether the model is statistically significant. Select whether each statement about the F test is correct or not correct.

a) The F test is a one-tail test.
b) The F test assesses whether the parameter ?0?is 0.
c) The test statistic used in the F test is the ratio of the regression mean square and the error mean square.



An investor plans to develop a regression model for the appraisal value (in thousands of dollars) of property in her city?(Y)?based on 5 numerical variables:

Y = ?0?+ ?1X1?+ ?2X2?+ ?3X3?+ ?4X4?+ ?5X5?+ ?

The investor would like to test whether or not the model has any significance. That is, she would like to test the hypotheses:

H0: ?1?= ?2?= ?3?= ?4?= ?5?= 0

HA: not all ?j?are zero

A sample of 30 items are drawn and the data is used to create the prediction equation:

y^?= b0?+ b1x1?+ b2x2?+ b3x3?+ b4x4?+ b5x5

The regression sum of squares (SSR) is calculated to be 378.4 and the error sum of squares (SSE) is calculated to be 518.4. An F test is conducted to test the above hypotheses.

a)Calculate the test statistic?(F)?for this test. Give your answer to 2 decimal places.

F =?

b)With a 99% level of confidence, the investor?cancannot?reject the null hypothesis.



You are part of a team investigating the identifying motor vehicle accidents. A multiple regression model is to be constructed to predict the number of motor vehicle accidents in a town per year based upon the population of the town, the number of recorded traffic offenses per year and the average annual temperature in the town.

Data has been collected on 30 randomly selected towns:?show data

a)Find the multiple regression equation using all three explanatory variables. Assume that X1?is population, X2?is number of recorded traffic offenses per year and X3?is average annual temperature. Give your answers to 3 decimal places.

y^?=??+?population +?no. traffic offences +?average temp

b)At a level of significance of 0.05, the result of the F test for this model is that the null hypothesis

isis not

rejected.

For parts?c)?and?d), using the data, separately calculate the correlations between the response variable and each of the three explanatory variables.

c)The explanatory variable that is most correlated with number of motor vehicle accidents per year is:

population
number of traffic offenses
average annual temperature

d)The explanatory variable that is least correlated with number of motor vehicle accidents per year is:

population
number of traffic offenses
average annual temperature

e)The value of R2?for this model, to 2 decimal places, is equal to?

f)The value of se?for this model, to 3 decimal places, is equal to?

g)Construct a new multiple regression model by removing the variable?average annual temperature. Give your answers to 3 decimal places.

The new regression model equation is:

y^?=??+?population +?no. traffic offences

h)In the new model compared to the previous one, the value of R2?(to 2 decimal places) is:

increased
decreased
unchanged

i)In the new model compared to the previous one, the value of se?(to 3 decimal places) is:

increased
decreased
unchanged


 


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