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Complete question:
Is there a relation between the age difference between husband/wives and the percent of a country that is literate? Researchers found the least-squares regression between age difference (husband age minus wife age), y, and literacy rate (percent of the population that is literate), x, is y' = -0.0445x + 7.2. The model applied for 25≤ x≤100. complete parts (a) through (e) below?
Select the correct choice below and fill in the answer box to complete your choice.
a) For every unit increase in ______ the ________falls by ____ units, on average. (Type an integer or decimal. Do not round.)
(b) Does it make sense to interpret the y-intercept? Explain. Choose the correct answer below.
A. Yes-it makes sense to interpret the y-intercept because an x-value of 0 is within the realm of possibilities.
B. No-it does not make sense to interpret the y-intercept because a y-value of 0 is outside the scope of the model.
C. No-it does not make sense to interpret the y-intercept because an x-value of 0 is outside the scope of the model.
(c) Predict the age diference between husband/wife in a country where the literacy rate is 39 percent years (Round to one decimal place as needed.)
(d) Would it make sense to use this model to predict the age difference between husband/wife in a country where the literacy rate is 10%?
A. Yes-it makes sense because an x-value of 10 is within the realm of possibilities and within the scope of the model.
B. No-it does not make sense because an x-value of 10 is outside the scope of the model.
C. No-it does not make sense because a y-value of 10 is outside the scope of the model.
D. Yes-it makes sense because a y-value of 10 is within the realm of possibilities and within the scope of the model.
(e) The literacy rate in a country is 98 % and the age difference between husbands and wives is 2 years. Is this age difference above or below the average age difference among all countries whose literacy rate is 98%? Select the correct choice below and fill in the answer box to complete your choice. (Round to one decimal place as needed.)
A. Below-the average age difference among all countries whose literacy rate is 98% is years. B. Above-the average age difference among all countries whose literacy rate is 98% is years
Answer:
a) For every unit increase in literacy rate the age difference falls by 0.0445 units, on average.
b) C. No-it does not make sense to interpret the y-intercept because an x-value of 0 is outside the scope of the model
c) 5.5
d) B. No-it does not make sense because an x-value of 10 is outside the scope of the model.
e) A. Below-the average age difference among all countries whose literacy rate is 98% is years.
Explanation:
Given:
y' = -0.0445x + 7.2
Where,
x = percentage of literate population
y = age difference between husband and wife
a) In this case, the regression equation is:
y' = -0.0445x + 7.2
The slope is -0.0445. This could be re-written as:
For every unit increase in literacy rate the age difference falls by 0.0445 units, on average.
b) Option C is correct because an x value of 0 is outside the scope of the model.
No-it does not make sense to interpret the y-intercept because an x-value of 0 is outside the scope of the model.
c) given, x = 39%
y' = -0.0445x + 7.2
Let's substitute 39 for x in the regression equation.
y' = -0.0445(39) + 7.2
y' = -1.7355 + 7.2
y' = 5.4645 ≈ 5.5
The age diference between husband/wife in a country where the literacy rate is 39 percent years is 5.5
d) When the literacy rate, x, is 10% it would not make sense to use this model to predict the age difference between husband & wife because the scope of the model(range) is 25≤x≤100. This means the xvalue of 10 is outside the scope of the model.
The correct option is B
B. No-it does not make sense because an x-value of 10 is outside the scope of the model.
e) For x = 98%
y' = -0.0445x + 7.2
Let's substitute 98 for x in the regression equation.
y' = -0.0445(98) + 7.2
y' = -1.7355 + 7.2
y' = 5.4645 ≈ 5.5
y' = 2.839
Option A is correct because 2.839 > 2.
A) Below-the average age difference among all countries whose literacy rate is 98% is years.
It should be noted that for every unit increase in the increase in literacy rate difference, the age difference falls by 0.0445 units on average.
The y-intercept should not be interpreted because it does not make sense to interpret the y-intercept because an x-value of 0 is outside the scope of the model.
The age difference where the literacy rate is 39% will be:
= (0.0445 × 39) + 7.2
= 1.7745 + 7.2
= 8.98
The model can be used to predict the age difference between the husband and wife when the literacy rate is 10% because a y-value of 10 is within the realm of possibilities and within the scope of the model.
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