Question

Consider the following data for two variables, x and y.

x	9	32	18	15	26
y	10	19	22	17	23

(a) Develop an estimated regression equation for the data of the form ŷ = b₀ + b₁x. (Round b₀ to two decimal places and b₁ to three decimal places.)

ŷ =

Comment on the adequacy of this equation for predicting y. (Use α = 0.05.)

The high p-value and low coefficient of determination indicate that the equation is inadequate.

The high p-value and high coefficient of determination indicate that the equation is adequate.  

  The low p-value and low coefficient of determination indicate that the equation is inadequate.

The low p-value and high coefficient of determination indicate that the equation is adequate.

(b) Develop an estimated regression equation for the data of the form ŷ = b₀ + b₁x + b₂x². (Round b₀ to two decimal places and b₁ to three decimal places and b₂ to four decimal places.)

ŷ =

Comment on the adequacy of this equation for predicting y. (Use α = 0.05.)

The high p-value and low coefficient of determination indicate that the equation is inadequate.

The high p-value and high coefficient of determination indicate that the equation is adequate.    

The low p-value and low coefficient of determination indicate that the equation is inadequate.

The low p-value and high coefficient of determination indicate that the equation is adequate.

(c) Use the model from part (b) to predict the value of y when x = 20.(Round your answer to two decimal places.)

Answer 1

(a)

Following is the output of regression analysis generated by excel:

The model is

The p-value of the model is 0.2098

Since p-value is large so model is not significant.

R square is 0.4576. Only 45.76% of variation in y is explained by X.

Correct option is

The high p-value and low coefficient of determination indicate that the equation is inadequate.

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Following table shows the data for x^2:

Y	X	x^2
10	9	81
19	32	1024
22	18	324
17	15	225
23	26	676

Following is the regression model:

The model is

The p-value of the model is 0.0269

Since p-value is small so model is significant.

R square is 0.9731. Only 97.31% of variaiton in y is exaplined by X.

Correct option is

The low p-value and high coefficient of determination indicate that the equation is adequate.

(c)

The model of part b is

Putting x=20 gives

Answer: 22.59