PROBLEM 4: A company that manufactures small lathes is interested in establishing standards for employees. A random sample of 18 employees is selected in order to develop the standards. The data collected is below. A manager at the firm feels that assembly time is related to intelligence. She feels that employees who did well in high school (as measured by high school averages) should be able to do the job faster. Does the data support her hunch? high school average Time to assemble lathe (minutes) 50 52 62 53 65 62 68 70 71 73 73 78 75 80 79 82 80 85 82 86 83 90 90 111 94 120 94 139 100 145
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.
- For the following problems, construct a
scatter plot using excel. After the plot is drawn, analyze it to determine which type of relationship, if any, exists. - For each of the following problems compute the
correlation coefficient r, r2, (show the intermediary steps) and summarize/explain the results.
PROBLEM 4:
A company that manufactures small lathes is interested in establishing standards for employees. A random sample of 18 employees is selected in order to develop the standards. The data collected is below.
A manager at the firm feels that assembly time is related to intelligence. She feels that employees who did well in high school (as measured by high school averages) should be able to do the job faster. Does the data support her hunch?
|
high school average
|
Time to assemble lathe (minutes) |
|
50 |
52 |
|
62 |
53 |
|
65 |
62 |
|
68 |
70 |
|
71 |
73 |
|
73 |
78 |
|
75 |
80 |
|
79 |
82 |
|
80 |
85 |
|
82 |
86 |
|
83 |
90 |
|
90 |
111 |
|
94 |
120 |
|
94 |
139 |
|
100 |
145 |
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