Question

part three: linear regression

1. use your calculator to input your fat (x) and calories (y) information for each find the equation of the line of best fit: y = mx + b

equation: y=12.97x + 116.3

1. find the correlation coefficient (r): 0.861
2. interpret the correlation: is it strong, weak, positive, negative, or none? explain.
3. what does the slope mean in the context of fast food items?
4. predict: use your equation above to predict the number of calories in a sandwich with 14 grams of fat. show your work.

part four: put your learning into words!
in a minimum of 5 sentences, summarize what you learned about linear regression in terms of correlation,
\ values, and trend lines. use good mathematical vocab.

Explanation:

Step1: Interpret correlation

The correlation coefficient $r = 0.861$. Since $r>0$, it is a positive correlation. Also, $|r|$ is close to 1 (ranging from - 1 to 1), so it is a strong correlation. This means as the fat content in fast - food items increases, the calorie content tends to increase strongly.

Step2: Interpret slope

The equation of the line is $y = 12.97x+116.3$, where the slope $m = 12.97$. In the context of fast - food items, for every additional gram of fat ($x$), the number of calories ($y$) increases by approximately 12.97 calories.

Step3: Predict calories

We have the equation $y = 12.97x + 116.3$ and $x = 14$. Substitute $x = 14$ into the equation:
$y=12.97\times14 + 116.3$
$y = 181.58+116.3$
$y=297.88$

Answer:

1. The correlation is strong and positive. A positive $r = 0.861$ value indicates that as the fat content in fast - food items increases, the calorie content increases, and since $|r|$ is close to 1, it is a strong relationship.
2. The slope of 12.97 means that for every additional gram of fat in a fast - food item, the number of calories increases by approximately 12.97 calories.
3. 297.88 calories.