(5.26) An owner o home in the Midwest installed solar panels to reduce heating c
ID: 3069006 • Letter: #
Question
(5.26) An owner o home in the Midwest installed solar panels to reduce heating costs. After installing he solar panels, he measured he amount of natural gas usedy in cubic tee to heat he om and outside temperaturez( in degree days, where a day's degree days are the number of degrees its average temperature falls below 65 F) over a 23 month period. He then computed the least squares regression line for predictingyfromxand found it to be 81 14x The predicted amount of gas used when the outside temperature is 25 degree-days is about: cubic feet. (Answer to the nearest cubic foot.) Hint (5.30) A study of king penguins looked for a relationship between how decp the penguins dive to seck food and how long they stay underwater. For all but the shallowest dives, there is a linear relationship that is different for different penguins. The study report gives a scatterplot for one penguin titled "The relation of dive duration (DD) to depth (D)" Duration DD is measured in minutes, and depth D is in meters. The report then says, "The regression equation for this bird is: DD-2.35 0.02 D." What is the slope of the regression linc? (Round your answer to the ncarest hundredth) This means that on average, If the length of the dive Increases by one meter, the diving duration increases by minutes. (Round your answer to the nearest hundredth.) According to the regression line, how long does a typical clive to a depth of 03 meters last?minutes. (Round your answer to the nearest tenth.) eBook Hint Check SExplanation / Answer
5.26
y = 81 + 14x
where y = Natural gas used (cubic feet.)
x = outside temp. ( degree days)
x = 25 degree days
y = 81 + 14(25)
= 81 + 350
= 431
5.30
Given equation : DD = 2.35 + 0.02D
The equation is in the form : y = mx +c
where m = slope of the equation
m = slope = 0.02
If lenghth increases by one meter , the diving duration increases by 0.02 minutes.
D = 203
DD = 2.35 + 0.02D
DD = 2.35 + 0.02(203)
= 6.4
PS : Please check if this is the correct equation I have used,
DD = 2.35 + 0.02D
As the "=" sign looks like a "-" sign.
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