part three: linear regression\n1. use your calculator to input your fat (x) and calories (y) information for…

part three: linear regression\n1. 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\nequation: y = 12.97x+1163\n2. find the correlation coefficient (r): 0.981\n3. interpret the correlation: is it strong, weak, positive, negative, or none? explain.\n4. what does the slope mean in the context of fast food items?\n5. predict: use your equation above to predict the number of calories in a sandwich with 14 grams of fat. show your work.\npart four: put your learning into words!\nin a minimum of 5 sentences, summarize what you learned about linear regression in terms of correlation, “r” values, and trend lines. use good mathematical vocab.

part three: linear regression\n1. 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\nequation: y = 12.97x+1163\n2. find the correlation coefficient (r): 0.981\n3. interpret the correlation: is it strong, weak, positive, negative, or none? explain.\n4. what does the slope mean in the context of fast food items?\n5. predict: use your equation above to predict the number of calories in a sandwich with 14 grams of fat. show your work.\npart four: put your learning into words!\nin a minimum of 5 sentences, summarize what you learned about linear regression in terms of correlation, “r” values, and trend lines. use good mathematical vocab.

Answer

Explanation:

Step1: Identify correlation coefficient interpretation

The correlation coefficient (r) values range from - 1 to 1. If (r) is close to 1, it's a strong positive correlation; close to - 1, strong negative; close to 0, weak.

Step2: Interpret given (r = 0.941)

Since (r=0.941) which is close to 1, it is a strong positive correlation. This means as the amount of fat in fast - food items increases, the number of calories also tends to increase significantly.

Step3: Interpret slope meaning

The slope (m = 12.97) in the equation (y=mx + b) (where (y) is calories and (x) is fat) means that for every additional gram of fat in a fast - food item, the number of calories increases by approximately 12.97.

Step4: Predict calories for 14 grams of fat

Substitute (x = 14) into the equation (y=12.97x+116.3). [y=12.97\times14 + 116.3] [y = 181.58+116.3] [y=297.88]

Answer:

  1. The correlation is strong and positive because the correlation coefficient (r = 0.941) is close to 1, indicating that as the fat content in fast - food items increases, the calorie content also increases significantly.
  2. The slope of 12.97 means that for each additional gram of fat in a fast - food item, the number of calories increases by approximately 12.97.
  3. The predicted number of calories in a sandwich with 14 grams of fat is 297.88.