Suppose a gas station monitors how many bags of ice they sell along with the maximum daily temperature for 100 days. A gas stati
on data analyst plots the data in a scatter plot with temperature, in °F, on the horizontal axis and the number of bags of ice sold on the vertical axis. She calculates a linear correlation coefficient of r = 0.9952 . The mean temperature is 84.1259 °F with a standard deviation of 9.6121 °F. The mean number of ice bags sold is 71.1173 with a standard deviation of 30.2413. Determine the slope, b , and the intercept, a , of the least-squares regression line for this dataset, precise to two decimal places.
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Answer: The required answers are
(a) the slope of the given line is
(b) y-intercept exists and is equal to 6.
(c) the slope-intercept form of the line is
Step-by-step explanation: We are given the following linear equation in two variables :
We are to :
(a) determine the slope,
(b) determine the y-intercept, if exists
and
(c) express equation in slope-intercept form.
We know that
The SLOPE_INTERCEPT form of the equation of a straight line is given by
where m is the slope and c is the y-intercept of the line.
From equation (i), we have
Comparing with the slope-intercept form, we get
Thus,
(a) the slope of the given line is
(b) y-intercept exists and is equal to 6.
(c) the slope-intercept form of the line is