Question

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

x	22	24	26	30	35	40
y	11	20	32	34	39	35

(a)

Develop an estimated regression equation for the data of the form

ŷ = b₀ + b₁x.

(Round b₀ to one decimal place and b₁ to three decimal places.)

ŷ =

(b)

Use the results from part (a) to test for a significant relationship between x and y. Use α = 0.05.

Find the value of the test statistic. (Round your answer to two decimal places.)

F =

Find the p-value. (Round your answer to three decimal places.)

p-value =

(c)

Develop an estimated regression equation for the data of the form

ŷ = b₀ + b₁x + b₂x².

(Round b₀ to one decimal place and b₁ to two decimal places and b₂ to four decimal places.)

ŷ =

(d)

Use the results from part (d) to test for a significant relationship between

x, x²,

and y. Use α = 0.05. Is the relationship between

x, x²,

and y significant?

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

Is the relationship between

x, x²,

and y significant?

Yes, the relationship is significant. No, the relationship is not significant.    

(e)

Use the model from part (d) to predict the value of y when

x = 25.

(Round your answer to three decimal places.)

Answer 1

Solved using excel data analysis tool for regression analysis

In excel-> Select data -> data analysis tool-> regression-> input X and Y

Answer(a) regression line is

Y=-7.8 +1.230*X

Answer(b) F value=6.85 and p-value =0.059

No, the relationship is not significant.

Answer(c)

regression equation is Y=-169.9+12.19*X-0.1770*X^2

Answer(d) P value=0.013

Yes, the relationship is significant.

Answer (e) predict y when X=25

Y=-169.9+12.19*25-0.1770*625=24.225