The equation of the least squares regression line is y^circ = 2.0233x-2.3256 and

Question

The equation of the least squares regression line is y^circ = 2.0233x-2.3256 and the sum of squared residuals for this line is 0.7907. Answer parts (a)- (d). Predict the mean value of y if x = 4 y^circ = _________(Round to one decimal place as needed.) Construct a 95% confidence in about the mean value of y if x = 4. Lower Bound =__________ Upper Bound = _________ (Round to one decimal place as needed.) Predict the value of y if x =4. y^circ = _________ (Round to one decimal place as needed.) Construct a 95% prediction interval about the value of y if x = 4. Lower Bound = __________ Upper Bound = _________ (Round to one decimal place as needed.)

Explanation / Answer

(a) 5.8

(b) Lower bound = 4.9, Upper bound = 6.7

(c) Lower bound = 3.9, Upper bound = 7.6.

Regression Analysis r² 0.989 n   5 r   0.994 k   1 Std. Error   0.513 Dep. Var. y ANOVA table Source SS   df   MS F p-value Regression 70.4093 1   70.4093 267.14 .0005 Residual 0.7907 3   0.2636 Total 71.2000 4   Regression output confidence interval variables coefficients std. error    t (df=3) p-value 95% lower 95% upper std. coeff. Intercept -2.3256 0.000 x 2.0233 0.1238 16.344 .0005 1.6293 2.4172 0.994 Predicted values for: y 95% Confidence Interval 95% Prediction Interval x Predicted lower upper lower upper Leverage 4 5.767 4.852 6.683 3.895 7.640 0.314

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