Question

the manager at a diner decided to see how the outside temperature affected soup sales. she looked at old receipts to see how the daily high temperature in degrees celsius, x, impacted the number of soup orders, y. then, she estimated a line of best fit.
the line of best fit has a y-intercept of 70 and a slope of -2.2.
based on this information, evaluate each statement.

	true	false
the number of soup orders increased by about 2.2 for every one-degree increase in the high temperature.
a 10°c increase in the high temperature would result in roughly 28 fewer soup orders.
if the high temperature was 30°c, the manager could expect to sell roughly 4 orders of soup.

Explanation:

Step1: Define the regression line

The line of best fit is $y = -2.2x + 70$, where $x$ = temperature (°C) and $y$ = soup orders.

Step2: Evaluate statement 1

Substitute $x=15$: $y = -2.2(15) + 70 = -33 + 70 = 37$. 37 ≠ 48 → False? Wait correction: Wait 70 - 2.2*15 = 70 -33=37, so original statement says 48 which is wrong → False? Wait no wait the first statement says 48, calculation gives 37 so it's False? Wait let's recheck:

Wait statement 1: 15°C → y= -2.2*15 +70= 70-33=37≠48 → False.

Statement2: Slope is -2.2 → orders decrease by 2.2 per 1°C increase → statement says increase → False.

Statement3: 10°C increase → change in y= -2.2*10= -22 → 22 fewer, not 28 → False.

Statement4: x=30 → y= -2.2*30 +70= -66+70=4 → this is True! Oh I missed that: 70-66=4 → yes, so statement4 is True.

So correct answers:

1. False
2. False
3. False
4. True

Step1: Regression equation setup

$y = -2.2x + 70$ (slope=-2.2, intercept=70).

Step2: Check statement 1 (x=15)

$y = -2.2(15)+70=37≠48$ → False.

Step3: Check statement2 (slope meaning)

Slope=-2.2 → orders decrease by 2.2 → False.

Step4: Check statement3 (10°C increase)

Δy=-2.2×10=-22≠-28 → False.

Step5: Check statement4 (x=30)

$y=-2.2×30+70=4$ → True.

Answer:

1. The diner sold approximately 48 orders of soup when the high temperature was 15°C: True
2. The number of soup orders increased by about 2.2 for every one-degree increase in the high temperature: False
3. A 10°C increase in the high temperature would result in roughly 28 fewer soup orders: False
4. If the high temperature was 30°C, the manager could expect to sell roughly 4 orders of soup: False