It appears that over the past 50 years the number of farms i

It appears that over the past 50 years, the number of farms in 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. Use these data to develop the equation of a regression line to predict the average size of a farm left-parenthesis y right-parenthesis by the number of farms left-parenthesis x right-parenthesis period Discuss the slope and y-intercept of the model.

(Do not round the intermediate values. Round your answers to 3 decimal places.)

Year	Number of Farms (millions)	Average Size (acres)
1950	5.68	214
1955	4.63	263
1960	3.96	300
1965	3.34	338
1970	3.00	379
1975	2.49	421
1980	2.44	426
1985	2.29	436
1990	2.16	459
1995	2.06	467
2000	2.17	432
2005	2.10	443
2010	2.20	422

Solution

It appears that over the past 50 years, the number of farms in 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. Use these data to develop the equation of a regression line to predict the average size of a farm left-parenthesis y right-parenthesis by the number of farms left-parenthesis x right-parenthesis period Discuss the slope and y-intercept of the model.

The regression line

Average size =591.266 - 69.742* number of farms

when the number of farms increased by 1(million), the average size decreased by 69.742(acres).

when the number of farms is 0, the average size is 591.266( acres).

( but interpretation of the y intercept is not appropriate or no meaning)

Regression Analysis

r²

0.973

n

13

r

-0.986

k

1

Std. Error

13.886

Dep. Var.

Average Size (acres)

ANOVA table

Source

SS

df

MS

F

p-value

Regression

76,191.9726

1  

76,191.9726

395.13

5.71E-10

Residual

2,121.1043

11  

192.8277

Total

78,313.0769

12  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=11)

p-value

95% lower

95% upper

Intercept

591.266

11.0865

53.332

1.24E-14

566.8649

615.6672

Number of Farms (millions)

-69.742

3.5085

-19.878

5.71E-10

-77.4641

-62.0197

Regression Analysis
	r²	0.973	n	13
	r	-0.986	k	1
	Std. Error	13.886	Dep. Var.	Average Size (acres)
ANOVA table
Source	SS	df	MS	F	p-value
Regression	76,191.9726	1	76,191.9726	395.13	5.71E-10
Residual	2,121.1043	11	192.8277
Total	78,313.0769	12
Regression output				confidence interval
variables	coefficients	std. error	t (df=11)	p-value	95% lower	95% upper
Intercept	591.266	11.0865	53.332	1.24E-14	566.8649	615.6672
Number of Farms (millions)	-69.742	3.5085	-19.878	5.71E-10	-77.4641	-62.0197