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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