Make a scatterplot for the data below on the number of people working on farms i

osi4a2nxk 2021-11-16 Answered
Make a scatterplot for the data below on the number of people working on farms in various years, and draw a line of best fit. Describe the correlation as strong positive, strong negative, or little to none.
\[\begin{array}{|c|c|}\hline Year & 1940 & 1950 & 1960 & 1970 & 1980 & 1990 \\ \hline \text{Number of farm workers in thousands} & 8995 & 6858 & 4132 & 2881 & 2818 & 2864 \\ \hline \end{array}\]

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Expert Answer

Blanche McClain
Answered 2021-11-17 Author has 227 answers

Step 1
Let x be the number of years after 1940. Then \(\displaystyle{x}={0}\) represents 1940, \(\displaystyle{x}={10}\) represents 1950, etc. Plot the points from the table as (Year, Number of workers):
image

Step 2
To find the line of best fit, enter \(\displaystyle{x}={0},\ {10},\ {20},\ {30},\ {40},\) and 50 under \(\displaystyle{L}_{{{1}}}\) in your graphing calculator and the corresponding number of workers under \(\displaystyle{L}_{{{2}}}\). Then use the linear regressions feature. This gives \(\displaystyle{y}=\approx-{126}{x}+{7903}\) as the line of best fit. Draw this line on your scatterplot. The correlation coefficient is \(\displaystyle{r}\approx-{0.91}\). Since the correlation coefficient is negative and close to -1, there is a strong negative correlation.
image
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