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 (y) by the number of farms (x). Discuss the slope and y-intercept of the model.

Year	Number of Farms (millions)	Average Size (acres)
1960	5.67	209
1965	4.66	258
1970	3.99	302
1975	3.38	341
1980	2.92	370
1985	2.51	419
1990	2.45	427
1995	2.28	439
2000	2.16	457
2005	2.07	471
2010	2.18	437
2015	2.10	442

(Do not round the intermediate values. Round your answers to 2 decimal places.)

y^=   +(   )x

Answer 1

we will solve this problem with the help of excel

let x denote the  number of farms(millions) and y denote the average size of a farm(acres)

Now steps to get the linear regression equation

1)1st we name two columns x and y then we input the values of x & y

2)we select the column of x and y

3) Go to "INSERT" menu then select the Scatter plot from the chart menu.

4) Now from the scatter plot menu select the 1st one the simple scatter plot

5) Here we get a scatter plot now beside the scatter plot we see a add option known as chart elements we select that

6) Now we select the option "Trendline" and then select the arrow beside Trendline

7)Then we get a few options and we select "More Options"

8) We get options under trendline option which is set to linear by default from there we select the option "Display Equation on chart"

9) We get scatter plot with trendline and linear regression equation(which can also be called regression line )

The equation we get is = -72.099x + 599.52

Answer:

Regression Line : = 599.52 - 72.10x [Rounded to 2 decimal place]

The slope indicates the mean change in the average size of a farm (y) in acres for an increase of 1 unit of the number of farms (x) in millions here the slope is -72.099 which means for 1 unit increase of x the y will decrease by 72.099 acres. [Here the y decreases as the slope is negative, it is (-) minus 72.099] and if the slope is negative then there is negative correlation between x and y which means i x increases y will decrease and vice versa.

y-intercept indicates the value of y when the variable x takes the value zero in this case it means the average size of a farm (y) when number of farms (x) is zero which does not make sense because if there are zero number of farms then there average size does not make sense so, we can say It is not appropriate to interpret the y-intercept because it does not make sense