Question

The table below shows the average daily temperature, x, and the number of dogs, y, that visited a dog park over the last nine days.

Temperature
(°F) Number of
Dogs
51 105
63 148
68 152
53 121
66 155
57 130
61 133
64 150
58 117

Calculate the correlation coefficient using technology. Then, select the correct statement.


The correlation coefficient is approximately 0.06 which means that there is not a significant increase in the number of dogs at the dog park with the increase in temperature.

The correlation coefficient is approximately 0.06 which means that there is a significant decrease in the number of dogs at the dog park with the increase in temperature.

The correlation coefficient is approximately 0.94 which means that there is a significant increase in the number of dogs at the dog park with the increase in temperature.

The correlation coefficient is approximately 0.94, but this does not represent causation since the increase in the number of dogs at the dog park is not likely caused by an increase in temperature.

Answer 1

it is explained below.

Explanation:

• the formula for correlation coefficient is given in the attachment.

• here, n=9

• 
  `\sum xy =`21*105 + 63*148 +........soooo on...

`\sum x =`51+63+68+......

`\sum y=`105+148+.......

`\sum x^(2) =`
`51^(2) +63^(2) +......`

`\sum y^(2) = 105^(2) + 148^(2) +......`

`(\sum x)^(2) = (51+63+68+.....)^(2)`

• now, substitute these values in the formula and calculate it using calculator.

• as we know that the range of correlation coefficient is -1 to 1 , if the obtained correlation coefficient is nearer to 1, then it means that there is a significant increase in the number of dogs at the dog park with the increase in temperature.

• if it is nearer to 0, then it means that there is a significant decrease in the number of dogs at the dog park with the increase in temperature.