P1 Math 220 Sp 2024

Project 1: Math 220 Dr. Hamdan Title: Analyzing the 2011 Home Sales Dataset Suppose an association of real estate professionals has reported home sales for 2011. The table contains the current sales by region and the inventory for existing homes. Download the data set with the name 2011_Home_Sales (1).xlsx from canvas (located under the Projects Module ) and save it to your desktop or your flash drive. Import the EXCEL dataset, 2011_Home_Sales (1).xlsx, to the SPSS: File>Import Data >EXCEL (Identify the file location then open ). Here is a description of the data Rows: 104 Columns: 4 Data Source: http://www.hawkeslearning.com/Statistics/dis/datasets.html Variables: Sales Price: The price that the home sold at Region: Region of the United States. NE= Northeast, MW= Midwest, S= South, W=West Home Type: The type of home described by ownership of the property and land surrounding the property Inventory: The amount of money that all the items inside the house are currently valued at 1

Questions (Copy your SPSS output to a word file and answer the questions- To copy anything form the SPSS Output window, just right click to use copy then paste) 1. How many variables does the dataset have? How many observations? Classify each variable as qualitative or quantitative. If the variable is qualitative, classify it as nominal or ordinal. If the variable is quantitative classify it as discrete or continuous. The dataset has 4 variables, 104 observations. Sale price is quantitative discrete, region is qualitative nominal, home type is qualitative nominal, and inventory is quantitative discrete. 2. Using the SPSS software, make a frequency table, a bar graph and a pie chart for the variable Region (make titles to your plots) Frequency table by region Frequenc y Percent Valid Percent Cumulative Percent Valid MW 26 25.0 25.0 25.0 NE 26 25.0 25.0 50.0 S 26 25.0 25.0 75.0 W 26 25.0 25.0 100.0 Total 104 100.0 100.0 2

4. Provide a numerical summary (using Analyze>Descriptives >Explore Select only Statistics at the bottom of the window under Display) (Of course with Explore you can get Graphical (Histogram, Stem-and-leaf, and Boxplot and Numerical summaries together ) Numerical Summary for sale price Statistic Std. Error Sale Price Mean 170627.88 4751.793 95% Confidence Interval for Mean Lower Bound 161203.82 Upper Bound 180051.94 5% Trimmed Mean 169942.95 Median 151200.00 Variance 2348271350.8 22 Std. Deviation 48458.966 Minimum 92400 Maximum 259300 Range 166900 Interquartile Range 89675 4

Skewness .404 .237 Kurtosis -1.316 .469 5. Describe the distribution of SalePrice (based on the histogram and numerical summaries) (e.g. is it symmetric or skewed to the right or left, is it unimodal, do you have outlier, is the standard deviation large …) The distribution of sale prices by frequency is slightly skewed right, bimodal with modes at $140,000-150,000 and $240,000-250,000 with no outliers. The standard deviation is 48,458.966, which isn’t abnormally high or low. 6. Provide a histogram for each region and a side-by-side boxplot for the SalePrice (using Analyze>Descriptives >Explore Move the Region variable to In the Factor List Select Plot s at the bottom of the window under Display. On the side and under Plots uncheck Stem-and Leaf and check Histograms ) 5

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7. Provide a numerical summary for the SalePrice for each region (using Analyze>Descriptives >Explore Move the Region variable to In the Factor List Numerical summary for the sale price by region Region Statistic Std. Error Sale Price MW Mean 135588.46 1349.442 95% Confidence Interval for Mean Lower Bound 132809.23 Upper Bound 138367.69 5% Trimmed Mean 135744.87 Median 135500.00 Variance 47345861.538 Std. Deviation 6880.833 Minimum 120600 Maximum 146700 Range 26100 Interquartile Range 8725 Skewness -.282 .456 Kurtosis -.472 .887 NE Mean 239323.08 1760.221 95% Confidence Interval for Mean Lower Bound 235697.83 Upper Bound 242948.32 5% Trimmed Mean 239002.14 Median 237500.00 Variance 80557846.154 Std. Deviation 8975.402 Minimum 225400 Maximum 259300 Range 33900 Interquartile Range 10250 Skewness .618 .456 Kurtosis .070 .887 S Mean 129011.54 4424.399 8

8. Using your answers in (6) and(7) compare and contrast the distribution of SalePrice in all regions(compare the shapes, the means and the standard deviations ) MW: The distribution is symmetric and almost looks approximately normal, with a mean sale price of 135588.46 and a standard deviation of 6880.833. NE: The distribution is skewed right, with a mean sale price of 239,323.08 and a standard deviation of 8975.402 S: W: 10