Question

Given the following quantities for a simple linear regression model results from a sample of size n=8 observations: ?x = 47.7, ?y = 324, ?x² = 304.59, ?y² = 14706, and ?xy = 1766.8 a) Use the above information to calculate SSxy, SSyy, and SSxx. (3 marks) b) Use the quantities in a) above to calculate ??? (1 mark) c) Calculate SSE and use it to calculate the estimated standard error of ???, s_???. (2 marks) d) Test H?: ?? = 0 against H?: ?? ? 0 at ? = 0.05 level of significance. (3 marks)

          Given the following quantities for a simple linear regression model results from a sample of size n=8 observations:

?x = 47.7, ?y = 324, ?x² = 304.59, ?y² = 14706, and ?xy = 1766.8

a) Use the above information to calculate SSxy, SSyy, and SSxx. (3 marks)

b) Use the quantities in a) above to calculate ??? (1 mark)

c) Calculate SSE and use it to calculate the estimated standard error of ???, s_???. (2 marks)

d) Test H?: ?? = 0 against H?: ?? ? 0 at ? = 0.05 level of significance. (3 marks)

Given the following quantities for a simple linear regression model results from a sample of size n=8 observations:

?x = 47.7, ?y = 324, ?x² = 304.59, ?y² = 14706, and ?xy = 1766.8

a) Use the above information to calculate SSxy, SSyy, and SSxx. (3 marks)

b) Use the quantities in a) above to calculate ??? (1 mark)

c) Calculate SSE and use it to calculate the estimated standard error of ???, s???. (2 marks)

d) Test H?: ?? = 0 against H?: ?? ? 0 at ? = 0.05 level of significance. (3 marks)

Added by Shelia M.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

05/03/2023

Step 1

7}{8} = 5.9625$ $\bar{y} = \frac{\sum y}{n} = \frac{324}{8} = 40.5$ Now, we can calculate the sum of squares: $SS_{xx} = \sum x^2 - n\bar{x}^2 = 304.59 - 8(5.9625)^2 = 42.715$ $SS_{yy} = \sum y^2 - n\bar{y}^2 = 14706 - 8(40.5)^2 = 1122$ $SS_{xy} = \sum xy - Show more…

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Given the following quantities for a simple linear regression model results from a sample of size n=8 observations: Σx = 47.7, Σy = 324, Σx² = 304.59, Σy² = 14706, and Σxy = 1766.8 a) Use the above information to calculate SSxy, SSyy, and SSxx. b) Use the quantities in a) above to calculate β̂₁ c) Calculate SSE and use it to calculate the estimated standard error of β̂₁, s_β̂₁. d) Test H₀: β₁ = 0 against Hₐ: β₁ ≠ 0 at α = 0.05 level of significance.