Question

1)An article reported that for a regression of y = average SAT score on x = expenditure per pupil, based on data from n = 44 New Jersey school districts, a = 766, b = 0.015, r² = 0.160, and s_e = 53.7. One observation in the sample was (9600, 892). What average SAT score would you predict for this district, and what is the corresponding residual?
Predict average SAT score _____
Residual _____

2) A paper concluded that there was a correlation between refined sugar consumption (calories per person per day) and annual rate of major depression (cases per 100 people) based on data from 6 countries. The following data were read from a graph that appeared in the paper. Compute the correlation coefficient for this data set. (Give the answer to three decimal places.)
r = ________

  

Country	Sugar Consumption	Depression Rate
Korea	140	2.4
United States	300	3.0
France	350	4.4
Germany	385	5.1
Canada	380	5.1
New Zealand	480	5.6

3) The following data on sale price, size, and land-to-building ratio for 10 large industrial properties appeared in a paper.

Property	Sale Price (millions of dollars)	Size (thousands of sq. ft.)	Land-to- Building Ratio
1	10.7	2166	1.9
2	2.5	752	3.6
3	30.5	2421	3.6
4	1.8	225	4.8
5	20.0	3916	1.6
6	7.9	2865	2.4
7	10.1	1699	3.0
8	6.6	1047	4.7
9	5.8	1107	7.7
10	4.5	405	17.3

(a) Calculate the value of the correlation coefficient between sale price and size. (Give the answer to three decimal places.)
r = _________

(b) Calculate the value of the correlation coefficient between sale price and land-to-building ratio. (Give the answer to three decimal places.)
r = _______

(d) Based on your choice in Part (c), find the equation of the least-squares regression line you would use for predicting y = sale price. (Give answers to three decimal places.)
= ________ + ________  x

Answer 1

Solution 1) Given, n =44, a = 766, b = 0.015, r^2 = 0.160, and se = 53.7.

One observation in the sample was (9600, 892)

Y(hat)= 766+0.015*X

X= 9600

Y(hat)= 766+0.015*9600

= 910

Predicted average SAT score is 910

Residual= y-y(hat)= 892-910= -18

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