Question

1. a local company is interested in studying transportation mobility among employees. the company interviewed all of the 200 employees and the questions were: employee responded as to whether or not they own a car and as to the location of the home where they live. the results are shown in the table below.

	own a car?
downtown area	10	60	70
in the city	15	55	70
outside the city	5	25	30
total	30	140	200

which of the following statements about a randomly chosen person from these 200 employees is true?
(a) if the person owns a car, he or she is more likely to live elsewhere in the city than to live in the downtown area or in the city.
(b) if the person does not own a car, he or she is more likely to live outside the city than to live in the city (downtown area or elsewhere) than if he or she lives in the river outside the city.
(c) the person is more likely to own a car if he or she lives in the downtown area or elsewhere) than if he or she lives in the river.
(d) the person is more likely to live in the downtown area in the city than elsewhere in the city.
(e) the person is more likely to own a car than not to own a car.

1. consider a pair of numbers (y_i, x_i), (x_2, y_2), ..., (x_n, y_n). the mean and standard deviation of the x-values are \\( \bar{x} = 5 \\) and \\( s_x = 3 \\). the mean and standard deviation of the y-values are \\( \bar{y} = 10 \\) and \\( s_y = 10 \\) respectively. of the following, which would be the least squares regression line?

(a) \\( \hat{y} = 5.0 + 3.0x \\)
(b) \\( \hat{y} = 1.0x \\)
(c) \\( \hat{y} = 5.0 + 2.5x \\)
(d) \\( \hat{y} = 4.5 + 0.3x \\)
(e) \\( \hat{y} = 10.0 + 0.6x \\)

1. the computer output below shows the result of a linear regression analysis for predicting the concentrations of zinc, in part per million (ppm), from the concentrations of lead, in ppm, found in fish from a certain river.

response variable is zinc (ppm)
constant	16.3	4.90	3.32	0.003
lead (ppm)	19.0	1.88	10.11	0.000
\\( s = 1n17 \\)	\\( r - sq = 82.0\\% \\)

what is the following statement is a correct interpretation of the value 19.0 in the output?

1. a census has been taken regarding the property to be new an old property. a random sample of 26 applied properties was selected. the following is a scatterplot of the property, in thousands of dollars, before and after the alteration. also shown is the least squares regression line and corresponding computer output.

(graph: scatter plot with old property value (thousands of dollars) on x - axis (0 - 400) and new property value (thousands of dollars) on y - axis (0 - 400), with a regression line. table:

term	coef	se coef	t - value	p - value
old property value	0.953597	0.10634	36.30	< 0.0001
\\( s = 7.53367 \\)	\\( r - sq = 88.75\\% \\)	\\( r - sq(adj) = 88.21\\% \\)

which of the following is not an appropriate description of the data in the sample?
(a) new property values tend to be greater than old property values.
(b) as old property values increase, new property values tend to increase.
(c) the relationship between old and new property value is strong and positive.
(d) for each additional $1,000 in old property value, the new property value increases by about $0.9536.
(e) the observed new property value typically deviate from the predicted new property value by about $7,534.

Explanation:

Step1: Identify the problem type

This problem involves linear regression analysis, specifically interpreting the coefficient of a predictor variable (Lead) in a regression model for predicting Zinc concentration. The key is to understand the meaning of the coefficient in the context of the regression equation.

Step2: Analyze the regression output

From the table, the coefficient for Lead (ppm) is 19.0, and the response variable is Zinc (ppm). The regression equation (implied) is related to predicting Zinc from Lead. The question is about the interpretation of the 19.0 value.

Step3: Recall regression coefficient interpretation

In a linear regression model \( \hat{y} = b_0 + b_1x \), \( b_1 \) represents the change in \( \hat{y} \) for a one - unit change in \( x \), holding other variables constant (though here Lead is a predictor for Zinc). So, for each 1 ppm increase in Lead, the predicted Zinc concentration changes by the coefficient of Lead.

Step4: Evaluate the options (implied from the problem's context)

Looking at the options (even though not fully visible, from the description), the correct interpretation should be about the change in Zinc concentration per unit change in Lead. The coefficient 19.0 means that for each 1 ppm increase in Lead, the predicted Zinc concentration increases by 19.0 ppm (or the relevant interpretation based on the model).

Answer:

The coefficient 19.0 in the output means that for each 1 ppm increase in the concentration of lead, the predicted concentration of zinc in the fish increases by 19.0 ppm (or the appropriate interpretation based on the full context of the options, e.g., if option (A) is "On average, there is a predicted increase of 19.0 ppm in concentration of zinc for every increase of 1 ppm in concentration of lead in the fish", then the answer would be that option).