A grocery store manager did a study to look at the relationship between the amount of time (in minutes) customers spend in the store and the amount of money (in dollars) they spend. The results of the survey are shown below. Time 22 16 15 19 7 8 14 10 Money 81 55 41 60 41 21 35 54
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.
PART TWO:
A grocery store manager did a study to look at the relationship between the amount of time (in minutes) customers spend in the store and the amount of money (in dollars) they spend. The results of the survey are shown below.
| Time | 22 | 16 | 15 | 19 | 7 | 8 | 14 | 10 |
|---|---|---|---|---|---|---|---|---|
| Money | 81 | 55 | 41 | 60 | 41 | 21 | 35 | 54 |
QUESTIONS 1-3 ARE ANSWERED
- Find the
correlation coefficient : r=.77 Round to 2 decimal places. - The null and alternative hypotheses for correlation are:
H0:H0: ? ρ = 0
H1:H1: ? ρ ≠ 0
The p-value is: .0205 (Round to four decimal places) - Use a level of significance of α=0.05α=0.05 to state the conclusion of the hypothesis test in the context of the study.
- There is statistically significant evidence to conclude that there is a correlation between the amount of time customers spend at the store and the amount of money that they spend at the store. Thus, the regression line is useful.
- r2 =______ (Round to two decimal places)
- Interpret r2r2 :
- Given any group that spends a fixed amount of time at the store, 60% of all of those customers will spend the predicted amount of money at the store.
- There is a 60% chance that the regression line will be a good predictor for the amount of money spent at the store based on the time spent at the store.
- 60% of all customers will spend the average amount of money at the store.
- There is a large variation in the amount of money that customers spend at the store, but if you only look at customers who spend a fixed amount of time at the store, this variation on average is reduced by 60%.
- The equation of the linear regression line is:
ˆy =_____ + _______x (Please show your answers to two decimal places)
Use the model to predict the amount of money spent by a customer who spends 13 minutes at the store.
Dollars spent = __________ (Please round your answer to the nearest whole number.) - Interpret the slope of the regression line in the context of the question:
- As x goes up, y goes up.
- For every additional minute customers spend at the store, they tend to spend on averge $2.66 more money at the store.
- The slope has no practical meaning since you cannot predict what any individual customer will spend
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