Question

1. Iman collected the average temperature in degrees Celsius along with the number of heaters that were sold at a local shop. What is the correlation coefficient of the data, and what does that tell you about the relationship between the two variables, or the line of best fit?

Month Temp. (C) Heaters Sold
Jan

-5 98
Feb -7 100
Mar 5 75
Apr 10 67
May 18 24
Jun 22 26
Jul 28 25
Aug 25 27
Sep 16 40
Oct 10 55
Nov 2 88
Dec -3 95


2. A researcher determined that the function to model men's weight based on height was this line of best fit:

LaTeX: f\left(x\right)=1.9x+40
f
(
x
)
=
1
.
9
x
+
40

where 'x' represents height in inches.

1. What does the 1.9 represent in the model?

2. What should be the weight of a man who is 71 inches tall?

Answer 1

Answer:Step by step is answer

Explanation:

To find the correlation coefficient and interpret the relationship between the two variables (temperature and heaters sold), we can use statistical software or a graphing calculator. Here is the table of the data with the calculated mean, standard deviation, and correlation coefficient:

Month Temp. (C) Heaters Sold

Jan -5 98

Feb -7 100

Mar 5 75

Apr 10 67

May 18 24

Jun 22 26

Jul 28 25

Aug 25 27

Sep 16 40

Oct 10 55

Nov 2 88

Dec -3 95

Mean: 10.5 - 53.5

Standard Deviation: 11.64 - 27.54

Correlation Coefficient: -0.76

The correlation coefficient, which ranges from -1 to +1, indicates the strength and direction of the linear relationship between the two variables. In this case, the correlation coefficient is negative, which means that as the temperature increases, the number of heaters sold decreases. The closer the correlation coefficient is to -1 or +1, the stronger the relationship is. In this case, the correlation coefficient of -0.76 suggests a moderate negative linear relationship between temperature and heaters sold.

Given the line of best fit for men's weight based on height:

f(x) = 1.9x + 40

(i) The coefficient 1.9 represents the slope of the line, which indicates the rate at which the weight changes with respect to height. Specifically, for every 1 inch increase in height, the predicted weight increases by 1.9 pounds.

(ii) To find the predicted weight of a man who is 71 inches tall, we can plug in x=71 into the equation and evaluate:

f(71) = 1.9(71) + 40 = 193.9

Therefore, the predicted weight of a man who is 71 inches tall is approximately 193.9 pounds.