HELP PLS!!Given the following data calculate the correlation coefficient. Then describe the correlation based on the correlation
2 answers:
I'm going to take the easy way, which is step by step, instead of trying to type out the formula for the correlation coefficient and then fill it in. It's way too complex. Step by step will be way simpler. First thing you have to do is find the mean of both x and y. The mean of x is 0+3+9+4+6 all divided by 5. That means that the mean of x is 4.4. For the mean of y: 11+26+17+22+18 all divided by 5. That means that the mean of y is 18.8. That's the first step. Second step is to find the standard deviation of x and y. That formula is . We would use the same formula to find the standard deviation for the y using the y coordinates and the mean of y. For the standard deviation for x we have
. Simplifying that down we have
and
which means that the standard deviation for x is 3.36. Now for y:
which simplifies down to
which means that the standard deviation for y is 5.63. Keep going...we're getting there. Now we need to take each coordinate pair x and y and multiply (x - mean(x))(y - mean(y)) and add those products together.
which simplifies down to
. Now divide that 13.4 by the product of the 2 standard deviation values: (3.36)(5.63):
. That quotient is .7083650512. Lastly, divide that number by n-1 or 4. That means that the correlation coefficient is .177. A really good correlation coefficient is close to 1. So .998 or even .863 is a good correlation. Our decimal is only .1, so the data is all over the place and the equation you could find on your calculator using the regression program would not fit these points very well at all.
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<em><u>Question # 1 Solution</u></em>
<em>Answer:</em>
32≤x≤48 is the best estimate for the amount of money, x, that Erika has to pay to get to her destination. Hence, option D is correct.
<em>Step-by-step Explanation:</em>
<em>Information Fetching and Solution Steps</em>
- Erika estimates that she is 200 to 300 miles away from her destination
- Car travels 25 miles per gallon of gas
- Cost of each gallon being $4.00
As Erika estimates that she is 200 to 300 miles away from her destination, and car travels 25 miles per gallon of gas. So,
- First dividing 200 by 25 to get the number of gallons a car needed to make 200 miles
i.e 200/25 = 8 gallons.
As cost of each gallon being $4.00.
So, 8 × 4 = 32$ is the amount she needed to make 200 miles.
- Then dividing 300 by 25 to get the number of gallons a car needed to make 300 miles
i.e 300/25 = 12 gallons.
As cost of each gallon being $4.00.
So, 12 × 4 = 48$ is the amount she needed to make 300 miles.
From the above calculation, we observe that 32$ and 48$ is the best estimate between 200 miles and 300 miles.
Therefore, 32≤x≤48 is the best estimate for the amount of money, x, that Erika has to pay to get to her destination. Hence, <em>option D</em> is correct.
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<em> </em><u><em>Question # 2 Solution</em></u>
<em>Answer:</em>
<em>Consultant B</em> offers the <em>cheapest price</em> for a <em>five hour session.</em>
Hence, <em>B. Consultant B</em> is the correct option.
<em>Step-by-step Explanation:</em>
<em>Analyzing the offer price of Consultant A, B and C for a Five hour session:</em>
<em />
- Consultant A chargers $160 for the first hour
- $75 per hour after the first.
So, for five hour session, Consultant A is offering the price:
$160 + $75 + $75 + $75 + $75 = $460
<em />
- Consultant B chargers a flat rate of $90 per hour
So, for five hour session, Consultant B is offering the price:
$90 + $90 + $90 + $90 + $90 = 450 US$
<em />
- Consultant C chargers $140 for the first hour
- $80 per hour after the first.
So, for five hour session, Consultant C is offering the price:
$140 + $80 + $80 + $80 + $80 = $460
<em>Comparing the price offers of Consultant A, B and C</em>
So, by comparing the price offers of Consultant A, B and C, we determine that:
- Consultant A is offering the price $460 for five hour session.
- Consultant B is offering the price $450 for five hour session.
- Consultant C is offering the price $460 for five hour session.
So, from this comparison, we conclude that <em>Consultant B</em> offers the <em>cheapest price</em> for a <em>five hour session.</em>
Hence, <em>B. Consultant B</em> is the correct option.
<em> </em>
<em> Question # 3 Solution</em>
<em>Answer:</em>
<em>They spent </em><em>4 nights</em><em> at the hotel. Hence, </em><em>option B</em><em> is correct.</em><em> </em>
<em>Step-by-step Explanation:</em>
<em>To determine: </em>
how many nights did they stay at the hotel?
<em>Information Fetching and Solution Steps</em>
- A hotel chargers $225 per night to rent a suite.
- The hotel also charges $75 per day for full room service.
- Jessica and Ashely purchased full room service for every night.
- They stayed at the hotel and spent a total of $1,200
As the total amount they spent = $1,200
As $75 is the service charges as Jessica and Ashely purchased full room service for every night.
Per night charges = hotel chargers + service charges
Per night charges = $225 + $75 ⇒ $300
So, total nights will be calculated as:
Total nights = total amount they spent ÷ Per night charges
Total nights = $1,200 ÷ $300 ⇒ 4 nights
<em>Therefore, they spent </em><em>4 nights</em><em> at the hotel. Hence, </em><em>option B</em><em> is correct.</em><em> </em>
<em />
<em> Question # 4 Solution</em>
<em>Answer:</em>
Hence, |h − 57.5| ≤ 7.5 is the absolute values which best represents this restriction, where ( h ) represents height. Hence, <em>option A</em><em> is correct.</em><em> </em>
<em>Information Fetching and Solution Steps</em>
- A certain ride at an amusement park requires that children be at least 50 inches tall but no more that 65 inches tall.
Let us take the equation of following absolute value:
|h − 57.5| ≤ 7.5
We know h − 57.5 ≤ and h − 57.5 ≥ −50
h − 57.5 ≤ 7.5 (Condition 1)
h − 57.5 + 57.5 ≤ 7.5 + 57.5 (Add 57.5 to both sides)
h ≤ 65
h − 57.5 ≥ −7.5 (Condition 2)
h − 57.5 + 57.5 ≥ −7.5 + 57.5 (Add 57.5 to both sides)
h ≥ 50
So, h ≤ 65 and h ≥ 50
Solution Graph is also attached as shown in attached figure a.
Hence, |h − 57.5| ≤ 7.5 is the absolute values which best represents this restriction, where ( h ) represents height. Hence, <em>option A</em><em> is correct.</em>
<em>Using same methodology we observe that all other options B, C, and D brings </em><em>wrong values </em><em>which is as follows:</em>
- <em>|h+7.5|≤65 brings h≤57.5 and h≥−72.5</em>
- <em>|h+50|≤65 brings h≤15 and h≥−115</em>
- <em>|h+65|≤50 brings h≤−15 and h≥−115</em>
Hence, from all discussion, we conclude that |h − 57.5| ≤ 7.5 is the absolute values which best represents this restriction, where ( h ) represents height, as it brings h ≤ 65 and h ≥ 50. Hence, <em>option A</em><em> is correct.</em>
Keywords: inequality, graph solution, absolute value
Learn more about inequality from brainly.com/question/11315582
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