It appears that over the past 50 years, the number of farms in the United States

Question

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

Explanation / Answer

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

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.