Solved:
Answered by AI, Verified by Human Experts
Consider the following data for two variables, x and y.
Consider the following data for two variables, x and y.x 22 24 26 30 35 40
y 13 20 34 35 39 37
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 = 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 a scatter diagram for the data. Does the scatter diagram suggast an estimated regression equation of the form y~=b0+b1x+b2x2z2 Explain. No, the scatter diagram suggests that a linear relationship may be appropriate. Yes, the scatter diagram suggests that a curvilinear relationship may be appropriate. Yes, the scatter diaaran suapests that a linear relationstip may be appropriate. Fo, tha scatter diagram suggests that a curvilinear relationship may be appropriato. (d) Develop an estimated regression equation for the date of the form y=bu+b1x+b2x2. (Round bu to one decimal pl y= (a) Wse the resulte from part (d) to test for a significant relationship hatween x,x2, and y. Use a=0.0.5. Is the relational Find the value of the test statistic. (Round rour answer to two decimal places.) Find the p-value. (Hound your answer to three decimal ploces.) p-value - Is tha ralationship between x,x2, and y significant? Yes, the relationahip is significant. Tvo, the relationstip is not significant. (f) Usa the model from part (d) to praclet the value of y when x=25. (Round your answar to three dacimal places.)
A. Develop an estimated regressionequationfor the data of the form ŷ = b0 + b1x. (Round b0 to one decimal place and b1 to threedecimalplaces.)Given data:x y22 1324 2036 3440 3545 3937 37The regression equation for the given data of the form ŷ = b0 + b1x is:y = b0 + b1xSince ŷ and y represent the same data, the equation is:ŷ = b0 + b1xTo find the values of b0 and b1, we use the following equations:Here, the values of x and y are substituted from the given data.The values of n, Ʃx, Ʃy, Ʃx2, and Ʃxy arecalculatedas shown below:n = 6Ʃx = 197Ʃy = 198Ʃx2 = 6,824Ʃxy = 6,533Now, we find the values of b0 and b1 as follows:b1 = [ nƩxy - (Ʃx)(Ʃy) ] / [ nƩx2 - (Ʃx)2 ]= [ (6 x 6,533) - (197 x 198) ] / [ (6 x 6,824) - (197)2 ]= 1.161b0 = [ (Ʃy) - b1(Ʃx) ] /n= [ 198 - (1.161)(197) ] / 6= 5.67Hence, the estimated regressionequationfor the given data is:ŷ = 5.67 + 1.161xB. Use the results from part (a) to test for asignificantrelationship between x and y. Use α = 0.05. Use the model from part (d) to predict the value of y whenx=25.Theestimatedregression equation for the given data is:y = 7.455 + 8.95E-05x + 0.001x2When x = 25,y = 7.455 + 8.95E-05(25) + 0.001(25)2= 8.697To know more aboutequationvisit:brainly.com/question/29657983#SPJ11...