We want to predict the selling price of a house in Newburg Park, Florida, based on the distance the house lies from the beach. Suppose that we're given the data in the table below. These data detail the distance from the beach (x, in miles) and the selling price (y, in thousands of dollars) for each of a sample of fifteen homes sold in Newburg Park in the past year. The data are plotted in the scatter plot in Figure 1. Also given is the product of the distance from the beach and the house price for each of the fifteen houses. (These products, written in the column labelled "xy", may aid in calculations.) Distance from the beach, x (in miles) Selling price, y (in thousands of dollars) xy 5.0 270.1 1350.5 11.5 205.9 2367.85 5.9 309.4 1825.46 12.2 200.6 2447.32 2.6 307.1 798.46 5.9 266.0 1569.4 8.3 297.3 2467.59 18.3 224.2 4102.86 6.5 242.4 1575.6 12.1 192.6 2330.46 11.6 229.4 2661.04 9.5 230.9 2193.55 10.1 277.0 2797.7 13.5 270.8 3655.8 6.2 217.2 1346.64 What is the slope of the least-squares regression line for these data? Carry your intermediate computations to at least four decimal places and round your answer to at least two decimal places.
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.
We want to predict the selling price of a house in Newburg Park, Florida, based on the distance the house lies from the beach. Suppose that we're given the data in the table below. These data detail the distance from the beach (x, in miles) and the selling price (y, in thousands of dollars) for each of a sample of fifteen homes sold in Newburg Park in the past year. The data are plotted in the
| Distance from the beach,
x
(in miles) |
Selling price,
y
(in thousands of dollars) |
xy
|
|---|---|---|
| 5.0 | 270.1 | 1350.5 |
| 11.5 | 205.9 | 2367.85 |
| 5.9 | 309.4 | 1825.46 |
| 12.2 | 200.6 | 2447.32 |
| 2.6 | 307.1 | 798.46 |
| 5.9 | 266.0 | 1569.4 |
| 8.3 | 297.3 | 2467.59 |
| 18.3 | 224.2 | 4102.86 |
| 6.5 | 242.4 | 1575.6 |
| 12.1 | 192.6 | 2330.46 |
| 11.6 | 229.4 | 2661.04 |
| 9.5 | 230.9 | 2193.55 |
| 10.1 | 277.0 | 2797.7 |
| 13.5 | 270.8 | 3655.8 |
| 6.2 | 217.2 | 1346.64 |
What is the slope of the least-squares regression line for these data? Carry your intermediate computations to at least four decimal places and round your answer to at least two decimal places.
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