A group of 11 students was selected at random and asked for their high school GPA and their freshmen GPA in college the subsequent year. The results were: Student High School GPA Freshmen GPA1 2.0 1.62 2.2 2.03 2.6 1.84 2.7 2.85 2.8 2.16 3.1 2.07 2.9 2.68 3.2 2.29 3.3 2.610 3.6 3.0I would like to know whether there is a linear relationship between the high school GPA and the college freshmen GPA, and we would like to be able to predict the freshmen GPA, if we know that the high school GPA of another student is, say, 3.4. answer the following questions, a-h. Then, provide the two requested scatter plots for this data (put college freshman GPA on the Y (vertical) axis!). Enter the data into Excel, (or whatever software you have and can use,) do the regression statistics (directions below), and Scatter Plot the data.a. What is the intercept?b. What is Beta (slope)?c. What is the SE?d. What is the p-value?e. What is the R-square?f. Is there a relationship between high school and college freshmen GPA’s? What is the actual equation of the least-square regression line?g. IF a high school student had a GPA 0f 3.0, what would you predict the college freshman GPA to be?h. What would be your approximate 95% prediction interval for question (g)?i. Copy/paste your scatter plot belowj. Copy/paste your scatterplot with the predicted trend line below
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
A group of 11 students was selected at random and asked for their high school GPA and their freshmen GPA in college the subsequent year. The results were:
Student High School GPA Freshmen GPA
1 2.0 1.6
2 2.2 2.0
3 2.6 1.8
4 2.7 2.8
5 2.8 2.1
6 3.1 2.0
7 2.9 2.6
8 3.2 2.2
9 3.3 2.6
10 3.6 3.0
I would like to know whether there is a linear relationship between the high school GPA and the college freshmen GPA, and we would like to be able to predict the freshmen GPA, if we know that the high school GPA of another student is, say, 3.4.
answer the following questions, a-h.
Then, provide the two requested scatter plots for this data (put college freshman GPA on the Y (vertical) axis!).
Enter the data into Excel, (or whatever software you have and can use,) do the regression statistics (directions below), and
a. What is the intercept?
b. What is Beta (slope)?
c. What is the SE?
d. What is the p-value?
e. What is the R-square?
f. Is there a relationship between high school and college freshmen GPA’s? What is the actual equation of the least-square regression line?
g. IF a high school student had a GPA 0f 3.0, what would you predict the college freshman GPA to be?
h. What would be your approximate 95% prediction interval for question (g)?
i. Copy/paste your scatter plot below
j. Copy/paste your scatterplot with the predicted trend line below
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