The following table shows the percentage of a country's residents over the age of 85 in 1950, 1960, ..., 2010. Year t 50 60 70 80 90 100 110 (years since 1900) Percentage P over 65 (%) 0.2 0.4 0.8 1.1 1.6 1.9 (a) Find the logarithmic regression model of the form P(t) = A In(t) + C. (Round the coefficients to four significant digits). HINT [See Example 4.] P(t) = (b) In 2020, 2.1% of the population is projected to be over age 85. To how many significant digits does the model reflect this figure? |significant digits (c) If you increase A by 0.1 and decrease C by 0.1 in the logarithmic model, then which of the following is correct? O The new model predicts eventually lower percentages. O The long-term prediction is essentially the same. O The new model predicts eventually higher percentages.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
![The following table shows the percentage of a country's residents over the age of 85 in 1950, 1960, ..., 2010.
Year t
50
60
70
80
90
100
110
(years since 1900)
Percentage P
over 65 (%)
0.2
0.4
0.8
1
1.1
1.6
1.9
(a) Find the logarithmic regression model of the form P(t) = A In(t) + C. (Round the coefficients to four significant digits). HINT [See Example 4.]
P(t) =
(b) In 2020, 2.1% of the population is projected to be over age 85. To how many significant digits does the model reflect this figure?
significant digits
(c) If you increase A by 0.1 and decrease C by 0.1 in the logarithmic model, then which of the following is correct?
The new model predicts eventually lower percentages.
O The long-term prediction is essentially the same.
O The new model predicts eventually higher percentages.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fca29bfd6-3149-45ff-96ff-c54d413a9a6d%2Fb4e1874f-6d20-42f2-aa6f-9845568fca68%2F7bufyqh_processed.png&w=3840&q=75)
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