Question

The following are advertised sale prices of color televisions at an electronics store.

Size (inches)	Sale Price ($)
9	137
20	187
27	297
31	447
35	1177
40	2177
60	2497

a) Calculate the least squares line. Put the equation in the form of: ŷ = a + bx.

(Round your answers to three decimal places.)

ŷ =___________+__________x

b) Find the correlation coefficient r. (Round your answer to four decimal places.)

r=____________

c) Find the estimated sale price for a 33 inch television. (Use your equation from part (d). Round your answer to two decimal places.)

$_____________

Find the estimated sale price for a 50 inch television. (Use your equation from part (d). Round your answer to two decimal places.)

$____________

d) What is the slope of the least squares (best-fit) line? (Round your answer to three decimal places.) ________________

Answer 1

From the given information, x? 20 Size Inches (x) Sale Price(y) 137 187 297 447 35 1177 40 2177 60 2497 Σx = 222 Ι Σy = 6919 27 31 xy 81 18769 1233 400 34969 3740 729 88209 8019 961 199809 13857 1225 1385329 41195 1600 4739329 87080 3600 6235009 149820 Σx2 = 8596 Σy? =12701423 Σxy = 304944 a). Calculate the least squares line. b-nΣy-ΣΧΣ η(Σ)-(Σx) 7(304944)- 222x6919 7(8596)-(222) = 54.9770389419544 = 54.977 (Round to 3 decimal place)

α- Σy -ΣΑ 6919-54.977 (222) =-755.128949301983 =-755.129 (Round to 3 decimal place) Hence, the required least square regression line is: lŷ = -755.129 + 54.977(x) Calculate the correlation coefficient (r) nΣχy -ΣΑΣ) [n(ΣΑ)-(Σx)][n(Σy)-(Σy)] 7(304944)- 222x6919 [7(8596) - (222) 17 (12701423)- (6919) ] = 0.89549977785666 (Round to 4 decimal place) = 0.8955 Hence, the required correlation coefficient is 0.8955).

Calculate the estimated sale price for a 33inch television. û = -755.129+54.977 (x) =-755.129+ 54.977 (33) = -755.129+1814.241 = 1059.112 = 1059.11 (Round to 2 decimal place) Hence, the required estimated sale price is: 1059.11. Calculate the estimated sale price for a 50inch television. û = -755.129 + 54.977(x) -755.129 + 54. =-755.129+2748.85 =1993.721 = 1993.72 (Round to 2 decimal place) Hence, the required estimated sale price is: 1993.72).

Calculate the slope of the least squares (best-fit) line. The least square regression line is: ġ=-755.129+ 54.977(x) The intercept coefficient is: a=-755.129 The intercept slope is: b = 54.977 Hence, the required slope coefficient is: b = 54.977)