Question

Consider the following data set that contains information about the average price of a gallon of milk in ten randomly chosen cities: Gas Price of a City price per gallon of milk gallon (5) (5) Atlanta 2.36 Tampa 2.72 2.92 St. Louis 3 Chicago Houston 3.12 Cincinnati 3.18 San Diego Kansas City 3.53 Detroit 3.8 3.67 Dallas 4.05 3.71 The scatter plot that summarizes the data with regard to price of gas as the input variable and price of a gallon of milk as the output variable is provided below. 3.07 3.04 20 . a. Is there an association between the two variables yes, is it positive or negative? There appears to be a Beed association between the two variables b. Use technology to find the equation of the line of best fit, y = mz+b, and the coefficient of determination and interpret the slope, the vertical intercept, and the coefficient of determination (Round the answers to 3 decimal places.) Lm Select an Select Select an awe hence there is a linear relation c. Use the line of best fit to: L. estimate the price of a gallon of milk when the price of gas is 3.15 dollars per gallon. Answer: dollars. Round the answer to 2 decimal places) estimate the price of gas when the price of gallon of milk is 3.16 dollars. Answer: dollars per gallon (Round the answer to 2 decimal places)

Answer 1

A)

there appears to be POSITIVE association beween two variables

...............

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	32.64	32.40	2.35	0.91	1.38
mean	3.26	3.24	SSxx	SSyy	SSxy

Sample size,   n =   10      
here, x̅ = Σx / n=   3.264          
ȳ = Σy/n =   3.240          
SSxx =    Σ(x-x̅)² =    2.3462      
SSxy=   Σ(x-x̅)(y-ȳ) =   1.4      
              
estimated slope , m = SSxy/SSxx =   1.3784/2.3462=   0.587

  
intercept,ß   = y̅-ß1* x̄ =   3.24- (0.5875 )*3.264=   1.322   
              
Regression line is, Ŷ=   1.322 + (   0.587   )*x

              
correlation coefficient ,    r = SSxy/√(SSx.SSy) =   0.941

hence there is positive relationship

R² =    (SSxy)²/(SSx.SSy) =    0.885

............

Predicted Y at X=   3.15   is          
Ŷ=   1.32242   +   0.58749   *3.15=   3.17

.................

3.16 = 1.32242   +   0.58749   *x

x =(3.16-1.322)/0.587
=3.13

.................

Please let me know in case of any doubt.

Thanks in advance!

Please upvote!