It appears that over the past 45 years, the number of farms I the United States declined while the average size of farms increased. The following data provided by the U.S. Department of Agriculture show five-year interval data for U.S. farms. Number of Farms (millions) 5.65 4.65 Average size (acres) 213 Year 1960 1965 258 1970 3.96 297 1975 3.36 340 1980 2.95 374 1985 2.52 420 1990 2.44 426 1995 2.29 441 2000 2.15 460 2005 2.07 469 2010 2.17 434 2015 2.10 444 i) Based on the output given, Use these data to develop the equation of a regression line to predict the average size of a farm by the number of farms. i) Explain the values of r and r. i) Predict the average size of a farm if the number of farms is 5.4 (millions). iv) Do the data support the existence of a linear relationship between the number of farms and the average size of a farm? Test using a 0.05.

It appears that over the past 45 years, the number of farms I the United States declined while the average size of farms increased. The following data provided by the U.S. Department of Agriculture show five-year interval data for U.S. farms. Number of Farms (millions) 5.65 4.65 Average size (acres) 213 Year 1960 1965 258 1970 3.96 297 1975 3.36 340 1980 2.95 374 1985 2.52 420 1990 2.44 426 1995 2.29 441 2000 2.15 460 2005 2.07 469 2010 2.17 434 2015 2.10 444 i) Based on the output given, Use these data to develop the equation of a regression line to predict the average size of a farm by the number of farms. i) Explain the values of r and r. i) Predict the average size of a farm if the number of farms is 5.4 (millions). iv) Do the data support the existence of a linear relationship between the number of farms and the average size of a farm? Test using a 0.05.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

It appears that over the past 45 years, the number of farms I the United States
declined while the average size of farms increased. The following data provided by
the U.S. Department of Agriculture show five-year interval data for U.S. farms.
Number of Farms
(millions)
5.65
Average size
(acres)
213
Year
1960
1965
4.65
258
1970
3.96
297
1975
3.36
340
1980
2.95
374
1985
2.52
420
1990
2.44
426
1995
2.29
441
2000
2.15
460
2005
2.07
469
2010
2.17
434
2015
2.10
444
i) Based on the output given, Use these data to develop the equation of a
regression line to predict the average size of a farm by the number of farms.
ii) Explain the values of r andr.
.
iii) Predict the average size of a farm if the number of farms is 5.4 (millions).
iv) Do the data support the existence of a linear relationship between the number
of farms and the average size of a farm? Test using a = 0.05.
OUTPUT
Model Summary
Adjusted R
Sid. Error of the
Model
R Square
Square
Estimate
988
975
973
14.02945
a. Predictors: (Constant), FARMS
ANOVA
Model
Sum of Squares
Mean Square
df
F
Sig
Regression
78078.411
78078.411
396.688
000
Residual
1968.255
10
196.826
Total
80046 667
11
a. Dependent Variable: SIZE
b. Predictors: (Constant), FARMS
Coefficients"
Standardized
Unstandardized Coefficients
Coefficients
Model
B
Std. Eror
Beta
Sig
(Constant)
600.186
11.711
51.251
.000
FARMS
-72.328
3.631
988
-19.917
000
a. Dependent Variable: SIZE

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