Question

Activity 1: Predicting prices of new homes

The dataset HomesForSale (available on Canvas) includes variables:
• State
• Price (in thousands $),
• Size (thousands square feet),
• Beds (number of bedrooms)
• Baths (number of bathrooms.

State Price Size Beds Baths
NJ 375 2.1 3 2.5
NJ 200 0.9 1 1
NJ 599 2.3 5 2.5
NJ 365 2.1 3 3
NJ 220 2.1 5 2
NJ 250 1.9 4 2.5
NJ 410 2.2 4 2.5
NJ 429 2.8 5 2.5
NJ 325 2 3 2.5
NJ 235 1.1 4 1
NY 145 1.3 3 1.5
NY 875 2.9 7 3.75
NY 300 1.5 3 2.5
NY 370 1.1 2 1
NY 268 1.5 2 2
NY 1399 4.8 6 5
NY 1125 3.1 3 2.5
NY 299 1.4 3 2
NY 110 1.2 3 1
NY 2999 6 7 8
PA 282 2.6 5 3.5
PA 135 1.3 2 2.5
PA 179 1.8 3 1
PA 800 3 3 4
PA 145 1.2 2 2
PA 170 1.6 3 3
PA 495 2.9 4 2.5
PA 224 1.5 2 2
PA 325 2.5 3 3
PA 180 1.9 1 1
PA 199 1.6 3 2

Open the dataset.

1. How many of these variables are quantitative? the response variable should be?


2. Make dotplots of the three predictor variables. Look at shape and the range of values for each predictor.


3. Fit a regression model using Size, Beds, and Baths to predict house price. What is the regression equation?


4. What is the predicted price for a house of size 2 thousand square feet with 3 bedrooms and 4 bathrooms? (Minitab hint: – use Stat à Regression à Regression à Predict

5. Which predictor appears to be the most effective predictor in the model (i.e., which is the most significant).

Answer 1

The dataset's quantitative variables are Price, Size, Beds, and Baths. A regression model can predict house prices using these variables, with the most effective predictor established by the lowest p-value. Actual analysis would provide specific values.

Step-by-step explanation:

Quantitative Variables and Regression Analysis

To answer the student's question regarding the dataset HomesForSale:

1. The quantitative variables in the dataset are Price, Size, Beds, and Baths. The response variable, in this case, would be the Price, as it is the outcome of interest we wish to predict.
2. Creating dotplots for the predictor variables Size, Beds, and Baths involves plotting each of these variables separately on the horizontal axis, with individual data points represented as dots along the vertical axis. This helps to visualize the distribution and range of values.
3. To fit a regression model using Size, Beds, and Baths to predict house price, one would typically use a software tool like Minitab or another statistical software package. The regression equation would generally look like Price (in thousands $) = a + b1*(Size in thousands sq ft) + b2*(Beds) + b3*(Baths), where a is the intercept and b1, b2, and b3 are the coefficients for the respective variables.
4. The predicted price for a house can be found by plugging the values into the regression equation obtained from the model. For example, if a house has a size of 2,000 square feet, 3 bedrooms, and 4 bathrooms, we would substitute these values into the regression equation to estimate the price.
5. The most effective predictor in the model can be determined by looking at the significance levels (p-values) for each coefficient in the regression analysis. The predictor with the smallest p-value (assuming it is below the typical alpha level of 0.05) is considered the most significant and thus the most effective predictor.

Keep in mind that the exact regression equation and effectiveness of the predictors would be determined by the actual data analysis, which would generate specific coefficients and significance levels.

Answer 2

The student's task is to analyze a dataset to predict the prices of homes using regression analysis. Various elements include determining the number of quantitative variables, creating dotplots, fitting a regression model, predicting prices based on the model, and identifying the most significant predictor in the model.

Step-by-step explanation:

The task involves analyzing a dataset to predict prices of new homes using variables such as state, price, size, beds, and baths. To achieve this, several steps are necessary:

• Determine the number of quantitative variables within the dataset - in this case, price, size, beds, and baths are all quantitative.
• Create dotplots for the predictor variables - size, beds, and baths - to understand their distribution and range.
• Fit a regression model with size, beds, and baths as predictor variables to determine the regression equation.
• Use the regression equation to predict the price of a house based on specific attributes.
• Identify the most effective predictor in the model by looking at the statistical significance of each.

For the practical task:

• The response variable is the price, which is dependent on the predictor variables size, beds, and baths.
• A dotplot would be made for each predictor variable to visualize the distribution of values.
• The regression equation is generally in the form ŷ = a + b1x1 + b2x2 + b3x3, where ŷ is the predicted price, and x1, x2, and x3 are size, beds, and baths, respectively.
• The predicted price for a house with given features could be calculated using the generated regression equation.
• Determining the most significant predictor would require looking at the p-values and coefficients of the regression output.