Determining the linear regression equation


Assignment:

A) Find the linear regression equation (line of best fit), determine the correlation, and then make a prediction.

1. The table below gives the amount of time students in a class studied for a test and their test scores. Graph the data on a scatter plot, find the line of best fit, and write the equation for the line you draw.

Hours Studied

1

0

3

1.5

2.75

1

0.5

2

Test Score

78

75

90

89

97

85

81

80

Linear Regression Equation:

Correlation Coefficient (r):

Type of Correlation:

Is the correlation strong? Explain

Using the linear regression equation predict astudents test score if they studied for 4 hours.

2. The table below gives the amount of Krabby Patties made by Spongebob for each year he's worked.

Graph the data on a scatter plot, find the line of best fit, and write the equation for the line you draw.

Years worked

1

2

3

4

5

6

Patties made

6,500

7,805

10,835

11,230

15,870

16,387

Linear Regression Equation:

Correlation Coefficient (r):

Type of Correlation:

Is the correlation strong? Explain

Using the linear regression equation predict how many Krabby Patties he will make after working 10 years.

3. The table below gives the estimated world population (in billions) for various years.

Year

1980

1990

1997

2000

2005

2011

Population

4400

5100

5852

6080

6450

7000

Linear Regression Equation:

Correlation Coefficient (r):

Type of Correlation:

Is the correlation strong? Explain

Using the linear regression equation predict the world population in the year 2015.

4. The table below shows the income for an employee over his first 8 years of work. Use this to estimate his income for his 15th year of work.

Years

1

2

3

4

5

6

7

8

Income

45,000

46,814

48,212

52,870

54,125

58,532

61,075

62,785

Linear Regression Equation:

Correlation Coefficient (r):

Type of Correlation:

Is the correlation strong? Explain

Using the linear regression equation predict his income for his 15th year of work.

B) Attached you will find an excel sheet data on the effect of 5 variables (Cylinder, displacement, horsepower, weight, seconds or acceleration) on the Gasoline consumption per 1000 miles. Based on the data please workout the following.

a) Regression model

b) Regression coefficient

c) Correlation coefficient between

- Gasoline consumption and cylinder

- Cylinder and displacement

- Gasoline consumption and acceleration

d) Find the p-value for

i. Total regression line

ii. Cylinder

iii. Displacement

iv. Horse power

v. Weight

vi. acceleration

e) identify the variable which has

i. a significant impact

ii. Less significant impact

f) Predict the Gasoline consumption per 1000 mile using the following data

i. Cylinder --- 6

ii. Displacement -- 2.2

iii. Horse power ---- 2.4

iv. Weight ---- 3.8

v. Acceleration - 12

Attachment:- Gasoline consumption Data.rar

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Microeconomics: Determining the linear regression equation
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