To find the correlation coefficient, slope of the regression line, and standard error for the model, we need to use regression analysis. Using a calculator, spreadsheet, or statistical software, we get:
a) The correlation coefficient is r ≈ 0.921.
b) The slope of the regression line is b ≈ 0.068.
c) The standard error for the model is SE ≈ 7.558.
d) Yes, there is a significant correlation between miles traveled and sales, since the correlation coefficient is close to 1, indicating a strong positive correlation.
e) The expected sales for a representative who travels 1000 miles in a month can be found by plugging x = 1000 into the regression line equation:
y = a + bx
where a is the y-intercept. To find a, we can use the formula:
a = y_bar - b x_bar
where y_bar is the mean of y values and x_bar is the mean of x values.
From the data given, we can calculate:
x_bar = (250 + 300 + 1240 + 720 + 840 + 1500 + 540 + 610 + 1300) / 9 ≈ 803.333
y_bar = (31 + 33 + 78 + 62 + 65 + 61 + 48 + 55 + 120) / 9 ≈ 63.333
Then, we can find:
b ≈ 0.068
a ≈ y_bar - b x_bar ≈ 63.333 - 0.068 * 803.333 ≈ 11.975
Finally, we can calculate:
y = 11.975 + 0.068 * 1000 ≈ 83
Therefore, the expected sales for a representative who travels 1000 miles in a month is about 83 thousand dollars.
it's a lot but your WELCOME!