Question

The table below gives the birth weights of five randomly selected mothers and the birth weights of their babies. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting the birth weight of a baby based on the mother's birth weight. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Mother 6.6 6.8 6.9 8 8.1 Baby 6.1 7.2 7.5 7.8 8.8 Step 1 of 6: Find the estimated slope. Round your answer to three decimal places. Step 2 of 6: Find the estimated y-intercept. Round your answer to three decimal places. Step 3 of 6: According to the estimated linear model, if the value of the independent variable is increased by one unit, then the change in the dependent variable yˆ is given by? . Step 4 of 6: Find the estimated value of y when x=6.8. Round your answer to three decimal places. Step 5 of 6: Find the error prediction when x=6.8. Round your answer to three decimal places. Step 6 of 6: Find the value of the coefficient of determination. Round your answer to three decimal places.

Answer 1

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
6.6	6.1	0.4624	1.9044	0.9384
6.8	7.2	0.2304	0.0784	0.1344
6.9	7.5	0.1444	0.0004	-0.0076
8	7.8	0.5184	0.1024	0.2304
8.1	8.8	0.6724	1.7424	1.0824

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	36.40	37.40	2.03	3.83	2.38
mean	7.28	7.48	SSxx	SSyy	SSxy

1)

sample size ,   n =   5          
here, x̅ = Σx / n=   7.280   ,     ȳ = Σy/n =   7.480  
                  
SSxx =    Σ(x-x̅)² =    2.0280          
SSxy=   Σ(x-x̅)(y-ȳ) =   2.4          
                  
estimated slope , ß1 = SSxy/SSxx =   2.4   /   2.028   =   1.173

2) intercept,   ß0 = y̅-ß1* x̄ =   -1.056

3) change in the dependent variable yˆ by slope = 1.173

4) Predicted Y at X=   6.8   is          
Ŷ =   -1.0564   +   1.1726   *6.8=   6.917

5)

residual = 7.2-6.917 = 0.283

6) R² =    (Sxy)²/(Sx.Sy) =    0.728