10.4

1) 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. Correct or Not Correct

b)The F test assesses whether the parameter ₀is 0. Correct or Not Correct

c)The test statistic used in the F test is the ratio of the regression mean square and the error mean square. Correct or Not Correct

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

H_A: not all _jare 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 268.8 and the error sum of squares (SSE) is calculated to be 548.5. 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 95% level of confidence, the investorcan or cannot reject the null hypothesis. ANSWER:_____

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 X₁is population, X₂is number of recorded traffic offenses per year and X₃is 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 hypothesisis or is notrejected. ANSWER:_____

For partsc)andd), 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:

A) population

B) number of traffic offenses

C) average annual temperature

ANSWER:______

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

A) population

B) number of traffic offenses

C) average annual temperature

ANSWER:_______

e)The value of R²for this model, to 2 decimal places, is equal to_______

f)The value of s_efor this model, to 3 decimal places, is equal to______

g)Construct a new multiple regression model by removing the variableaverage 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:

A) increased

B) decreased

C) unchanged

ANSWER:______

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

A) increased

B) decreased

C) unchanged

ANSWER:______