4. Trying to determine the number of students to accept is a tricky task for universities. The Admissions staff at a small private college wants to use data from the past few years to predict the number of students enrolling in the university from those who are accepted by the university. R INPUT: accepted <- c(2440,2800,2720,2360,2660,2619) enrolled <-c(611,708,637,584,614,624) fit <- 1m(enrolled accepted) summary(fit) R OUTPUT: Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 88.88272 182.36584 0.487 0.6515 accepted 0.20801 0.07002 2.971 0.0411 * --- Signif. codes: O **** 0.001 '**' 0.01 (*' 0.05 '.’ 0.1 ' ' 1 Residual standard error: 26.35 on 4 degrees of freedom Multiple R-squared: F-statistic: 8.824 on 1 and 4 DF, 0.6881, Adjusted R-squared: 0.6101 p-value: 0.04112 (a) Write an equation for the regression line. (b) What is the slope of the least-squares regression line? Interpret this in the context of the application. (c) Interpret the intercept of the line in context. Does the interpretation make sense?
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
![4. Trying to determine the number of students to accept is a tricky task for universities.
The Admissions staff at a small private college wants to use data from the past few
years to predict the number of students enrolling in the university from those who are
accepted by the university.
R INPUT:
accepted <- c(2440,2800,2720,2360,2660,2619)
enrolled <-c(611,708,637,584,614,624)
fit <- lm(enrolled
accepted)
summary(fit)
R OUTPUT:
Coefficients:
Estimate Std. Error t value Pr(>|t])
(Intercept)
accepted
88.88272
182.36584
0.487
0.6515
0.20801
0.07002
2.971
0.0411 *
Signif. codes:
***' 0.001 **' 0.01 '*' 0.05 '.' 0.1 ' 1
Residual standard error: 26.35 on 4 degrees of freedom
0.6881,
Adjusted R-squared:
0.6101
Multiple R-squared:
F-statistic: 8.824 on 1 and 4 DF, p-value: 0.04112
(a) Write an equation for the regression line.
(b) What is the slope of the least-squares regression line? Interpret this in the context
of the application.
(c) Interpret the intercept of the line in context. Does the interpretation make sense?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7237bf46-4025-4c4f-b170-df7369a74fb6%2Fc2e82a97-030b-4802-a57d-c3af08894dbf%2Fwp3iits_processed.png&w=3840&q=75)
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