9) We have a sample of 6 observations on exam scores and hours of study and would like to estimate the following relationship using the least-squares method: Score = Bo + Bi hours + e. We expect the score to increase with hours of study. Score 80 90 85 65 50 80 Hours 12 14 11 10 8 11 Σscore 450 Σλοurs 6, Σ hours. score 5085 , Σ score= 34850, Σhours 746 a. Estimate the unknown parameters using the method of OLS and find the least-squares prediction equation. b. Calculate SSF, R², standard error of the residuals (s), and standard error of slope coefficient (s3,). Construct and interpret a 90% confidence interval for Bi. c. Predict the score of a student who studies 9 hours for the exam, and construct and interpret a 90% confidence interval using the predicted value (prediction interval).
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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