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Suppose a gas station monitors how many bags of ice they sell along with the maximum daily temperature for 100 days. A gas station 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.

Answer :

Answer:

Slope=b= 2.46

Intercept=a= -135

No. of bags sold= 78 at 87 F temperature

Complete solution with calculation is given in the pictures attached.

${teks-lihat-gambar} hamzafarooqi188
${teks-lihat-gambar} hamzafarooqi188
MrRoyal

The bags of ice and the temperature are illustrations of linear regression

  • The slope is 3.13
  • The y-intercept is -192.20

The given parameters are:

[tex]\mathbf{n = 100}[/tex] -- the sample size

[tex]\mathbf{r = 0.9952}[/tex] -- the correlation coefficient

[tex]\mathbf{\bar x = 84.1259}[/tex] --- the mean temperature

[tex]\mathbf{\sigma_x = 9.6121}[/tex] --- the standard deviation temperature

[tex]\mathbf{\bar y = 71.1173 }[/tex] --- the mean ice bags

[tex]\mathbf{\sigma_y = 30.2413 }[/tex] --- the standard deviation ice bags

(a) The slope

The slope is calculated as:

[tex]\mathbf{b =r \times \frac{\sigma_y}{\sigma_x}}[/tex]

So, we have:

[tex]\mathbf{b =0.9952 \times \frac{30.2413}{9.6121}}[/tex]

[tex]\mathbf{b =3.13}[/tex]

Hence, the slope is 3.13

(b) The intercept

The y-intercept is calculated as:

[tex]\mathbf{a = \bar y - b \times \bar x}[/tex]

So, we have:

[tex]\mathbf{a = 71.1173 - 3.13 \times 84.1259 }[/tex]

[tex]\mathbf{a = -192.20}[/tex]

Hence, the y-intercept is -192.20

Read more about slopes and intercepts of a regression equation at:

https://brainly.com/question/21565131

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