Question

Consider the following data for two variables,  and .

x	8	27	21	16	22
y	8	30	23	12	26

a. Develop an estimated regression equation for the data of the form y=b0+b1x . Comment on the adequacy of this equation for predicting . Enter negative value as negative number.

The regression equation is

Y=_______+_______ (to 2 decimals)

s= (to 3 decimals) R^2= % (to 1 decimal) R^2 adj= % (to 1 decimal)

Analysis of Variance

SOURCE DF SS (to 2 decimals) MS (to 2 decimals) F (to 2 decimals) -value (to 4 decimals) Regression Residual Error Total

Using a .05 significance level, the p-value indicates a - Select your answer -weak relationship strong relationship no relationship ; note that  (to 1 decimal) of the variability in  has been explained by .

b. Develop an estimated regression equation for the data of the form y=b0+b1x+b2x^2. Comment on the adequacy of this equation for predicting y . Enter negative value as negative number. If your answer is zero, enter "0".

The regression equation is

Y=______+_____x+______x^2 (to 2 decimals)

S= (to 3 decimals) R^2= % (to 1 decimal) R^2 adj= % (to 1 decimal)

Analysis of Variance

SOURCE DF SS (to 3 decimals) MS (to 3 decimals) (to 2 decimals) -value (to 4 decimals) Regression Residual Error Total

At the .05 level of significance, the relationship - Select your answer -is/ is not significant; note that   (to 1 decimal) of the variability in  has been explained by .

c.Using the appropriate regression model, predict the value of y when x=17 .

(to 2 decimals)

Answer 1

a) Answer

The regression equation is
y = - 3.82 + 1.26 x

S = 2.967       R-Sq = 92.5%     R-Sq(adj) = 90.0%

Analysis of Variance

Source            DF          SS          MS         F        P
Regression         1      326.38      326.38     37.07    0.009
Residual Error     3       26.42        8.81
Total                   4      352.80

using 0.05 significance level, p-value indicates strong relationship

b) Answer

The regression equation is
y = 2.5 + 0.38 x + 0.0254 x²

S = 3.285       R-Sq = 93.9%     R-Sq(adj) = 87.8%

Analysis of Variance

Source            DF          SS          MS         F        P
Regression         2      331.22      165.61     15.35    0.061
Residual Error     2       21.58       10.79
Total              4      352.80

using 0.05 significance level, p-value indicates weak relationship.

Since model in a) represents strong relationship, hence using model in a) the value of y when x=17

is y= -3.82+ 1.26*17= 17.6