A consumer buying cooperative tested the effective heating area of 20 different

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A consumer buying cooperative tested the effective heating area of 20 different electric space heaters with different wattages. Here are the results. Heater Wattage Area 1 1,750 85 2 1,500 225 3 2,000 177 4 2,000 205 5 1,750 289 6 1,500 79 7 1,000 136 8 1,250 162 9 2,000 120 10 1,250 242 11 2,000 292 12 1,000 221 13 1,250 270 14 1,250 73 15 2,000 286 16 2,000 70 17 2,000 111 18 1,250 290 19 1,000 138 20 1,500 137 PictureClick here for the Excel Data File a. Compute the correlation between the wattage and heating area. Is there a direct or an indirect relationship? (Negative values should be indicated by a minus sign. Round your answer to 3 decimal places.) The correlation of Wattage and Area is . The link (relationship) is . b. Conduct a test of hypothesis to determine if it is reasonable that the coefficient is greater than zero. Use the 0.025 significance level. (Negative values should be indicated by a minus sign. Round your answer to 3 decimal places.) H0: 0; H1: > 0. Reject H0 if t > 2.101 t = H0. It is to say the population correlation is positive. c. Develop the regression equation for effective heating based on wattage. (Negative values should be indicated by a minus sign. Round your answers to 3 decimal places.) The regression equation is: = + . d. Which heater looks like the “best buy” based on the size of the residual? (Round residual value to 2 decimal places.) The heater is the "best buy." It heats an area that is square feet larger than estimated by the regression equation.

A suburban hotel derives its revenue from its hotel and restaurant operations. The owners are interested in the relationship between the number of rooms occupied on a nightly basis and the revenue per day in the restaurant. Below is a sample of 25 days (Monday through Thursday) from last year showing the restaurant income and number of rooms occupied.

A suburban hotel derives its revenue from its hotel and restaurant operations. The owners are interested in the relationship between the number of rooms occupied on a nightly basis and the revenue per day in the restaurant. Below is a sample of 25 days (Monday through Thursday) from last year showing the restaurant income and number of rooms occupied.

Explanation / Answer

1)

= ( XY - X Y / n ) / SQRT { [ X^2 - (X)^2 / n] [ Y^2 - (Y)^2 / n]}

Since the r is positive the relation is DIRECT RELATION SHIP

SInce p > 0.95, we reject null hypothsis

approximately slope is equal

c) Based on the intercept and slope

y = -0.00288525 x+ 184.9

d) The one with lowest wattage is preferable according to inverse slope, but according to data, r is too weak to deine a relation between two variables

heater wattage(x) area(y) xy x^2 y^2 1 1750 85 148750 3062500 7225 2 1500 225 337500 2250000 50625 3 2000 177 354000 4000000 31329 4 2000 205 410000 4000000 42025 5 1750 289 505750 3062500 83521 6 1500 79 118500 2250000 6241 7 1000 136 136000 1000000 18496 8 1250 162 202500 1562500 26244 9 2000 120 240000 4000000 14400 10 1250 242 302500 1562500 58564 11 2000 292 584000 4000000 85264 12 1000 221 221000 1000000 48841 13 1250 270 337500 1562500 72900 14 1250 73 91250 1562500 5329 15 2000 286 572000 4000000 81796 16 2000 70 140000 4000000 4900 17 2000 111 222000 4000000 12321 18 1250 290 362500 1562500 84100 19 1000 138 138000 1000000 19044 20 1500 137 205500 2250000 18769 Sum 210 31250 3608 5629250 51687500 771934

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