Deaths The number of deaths in traffic accidents Income The average income per f

Question

Deaths

The number of deaths in traffic accidents

Income

The average income per family

Children

The number of children (in multiples of 100,000) between the ages

of 1 and 14 in the state

As part of his investigation he ran the multiple regression model,

Deaths = 0 + 1(Children) + 2(Income) + i,

where the deviations i were assumed to be independent and Normally distributed with a mean of 0 and a standard deviation of . This model was fit to the data using the method of least squares. The following results were obtained from statistical software.

Source

Sum of squares

df

Model

48362278

2

Error

3042063

48

Variable

Coefficient

Standard error

Constant

593.829

204.114

Children

90.629

3.305

Income

–0.039

0.015

The researcher also ran the simple linear regression model

Deaths = 0 + 2(Income) + i.

The following results were obtained from statistical software:

Source

Sum of squares

df

Model

711680

1

Error

50692661

49

Variable

Coefficient

Standard error

Constant

292.518

823.505

Income

0.050

0.060

What is the value of R2 in the simple linear regression model?

Please explain how the answer is 0.014

I have been told that is the correct answer I am just struggling to find it.

. A researcher is investigating possible explanations for deaths in traffic accidents. He examined data from 1991 for each of the 50 states plus Washington, DC. The data included information on the following variables.

Deaths

The number of deaths in traffic accidents

Income

The average income per family

Children

The number of children (in multiples of 100,000) between the ages

of 1 and 14 in the state

As part of his investigation he ran the multiple regression model,

Deaths = 0 + 1(Children) + 2(Income) + i,

where the deviations i were assumed to be independent and Normally distributed with a mean of 0 and a standard deviation of . This model was fit to the data using the method of least squares. The following results were obtained from statistical software.

Source

Sum of squares

df

Model

48362278

2

Error

3042063

48

Variable

Coefficient

Standard error

Constant

593.829

204.114

Children

90.629

3.305

Income

–0.039

0.015

The researcher also ran the simple linear regression model

Deaths = 0 + 2(Income) + i.

The following results were obtained from statistical software:

Source

Sum of squares

df

Model

711680

1

Error

50692661

49

Variable

Coefficient

Standard error

Constant

292.518

823.505

Income

0.050

0.060

What is the value of R2 in the simple linear regression model?

Please explain how the answer is 0.014

I have been told that is the correct answer I am just struggling to find it.

Explanation / Answer

What is the value of R2 in the simple linear regression model?

Please explain how the answer is 0.014

Source

Sum of squares

df

Model

711680

1

Error

50692661

49

Total

51404341

Total sum of squares = Modes SS +Error SS

=711680+50692661

=51404341

R2 = Model SS / Total SS

=711680/ 51404341

= 0.013845

=0.014 ( rounded to 3 decimals)

Source

Sum of squares

df

Model

711680

1

Error

50692661

49

Total

51404341

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