For a sample of 306 students in a basic business statistics course, the sample regression liney = 58.813 + 0.2875xwas obtained. Here,y = final student score at the end of the coursex = score on a diagnostic statistics test given at the beginning of the courseThe coefficient of determination was 0.1158, and the estimated standard deviation of the estimator of the slope of the population regression line was 0.04566.a. Interpret the slope of the sample regression line.b. Interpret the coefficient of determination.c. The information given allows the null hypothesis that the slope of the population regression line is 0 to be tested in two different ways against the alternative that it is positive. Carry out these tests and show that they reach the same conclusion.
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.
For a sample of 306 students in a basic business statistics course, the sample regression line
y = 58.813 + 0.2875x
was obtained. Here,
y = final student score at the end of the course
x = score on a diagnostic statistics test given at the beginning of the course
The coefficient of determination was 0.1158, and the estimated standard deviation of the estimator of the slope of the population regression line was 0.04566.
a. Interpret the slope of the sample regression line.
b. Interpret the coefficient of determination.
c. The information given allows the null hypothesis that the slope of the population regression line is 0 to be tested in two different ways against the alternative that it is positive. Carry out these tests and show that they reach the same conclusion.
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