1. TJ just had his first \'at fault\' accident, and he is concerned about the ef
ID: 3116488 • Letter: 1
Question
1. TJ just had his first 'at fault' accident, and he is concerned about the effecet on his annual insurance premium. He found that his insurance company has data about number of at fault' accidents (x) and the cost of the annual premium (v). They noted that graphing the data as ordered pairs shows a line that fits the equation y $350 x +$1500. [TJ had learned in his statistics class that fitting a line to data is called linear regression.] a) What is the slope of the line given, and what does it mean for this situation b) What is the y-intercept for this line, and what does it mean for this situation? Using this line, find the y value when x -3. Give the meaning of this y value in the context of this situation. c) A study found that the number of times students texted during the review class and the grade on their Psychology tests has a linear relationship where x represents the number of texts sert and y, the test score. A student who sent no texts scored a 92, and another student who sent 8 texts scored a 60. 2. Write the information in the problem as two ordered pairs where x represents the number of texts sent and y is the test grade. a) b) Write the equation of the line that passes through these two points A line that best fits data is called a regression line. Such a line can be used to make predictions about your y value based on reasonable x values. Using this equation from part (b) what would you predict to be the Psychology test score if 15 texts were sent? c)Explanation / Answer
1. Comparing the given equation with the standard form of straight line in slope-intercept form
y= mx + c, where m is the slope and c is the intercept we have
a) Slope = $ 350. In given case it represents that for each at fault accident, the annual premium increases by $350.
b) Y intercept for this line = $1500. In given case, it represents when number of at fault accidents is zero, the annual premium is $ 1500.
c) Putting x=3, we have, y = $350×3+$1500 = $2550.
In given situation it implies that when at fault accident is 3 then annual premium becomes $2550.
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