1). Mulberry Realty sells homes in the northeast section of the United States. A
ID: 3267173 • Letter: 1
Question
1). Mulberry Realty sells homes in the northeast section of the United States. A frequently asked question by prospective buyers is: If we buy this house, how much can we expect to pay to heat it during the winter? The research division of Mulberry is asked to develop some guidelines for heating costs (Cost) (measured in $) for single family homes. The division decides three variables are related to heating costs: (1) the mean daily outside temperature (Temp) (in degrees Fahrenheit); (2) the number of inches of attic insulation (Insulation); and (3) the age of the furnace in the house (Age) (measured in years). The division collected data during the month of January for a sample of homes. Parentheses contain the variable names (in bold) as listed in the data set. a. Is the information used in this analysis, cross-sectional data or time series data? (4 pts) b. State you’re a priori hypothesis about the sign of the slope for each independent variable. (3 pts each) c. Write out the estimated regression equation using variable specific names? (5 pts) d. Interpret the slope coefficient for the variable with the largest slope coefficient. (5 pts) e. For the slope coefficient with the smallest value (in absolute value), test to see if it has the directional relationship hypothesized in part (b). Alpha = 0.05. (15 pts) f. Construct and interpret a 98% confidence interval for the largest slope coefficient (in absolute value). (9 pts) g. Interpret the coefficient of determination. (5 pts) a. Is the information used in this analysis, cross-sectional data or time series data? (4 pts) b. State you’re a priori hypothesis about the sign of the slope for each independent variable. (3 pts each) c. Write out the estimated regression equation using variable specific names? (5 pts) d. Interpret the slope coefficient for the variable with the largest slope coefficient. (5 pts) e. For the slope coefficient with the smallest value (in absolute value), test to see if it has the directional relationship hypothesized in part (b). Alpha = 0.05. (15 pts) f. Construct and interpret a 98% confidence interval for the largest slope coefficient (in absolute value). (9 pts) g. Interpret the coefficient of determination. (5 pts)
Cost ($) Temp (deg) Insulation (ins.) Age (yrs) 250 35 3 6 360 29 4 10 165 36 7 3 43 60 6 9 92 65 5 6 200 30 5 5 355 10 6 7 290 7 10 10 230 21 9 11 120 55 2 5 73 54 12 4 205 48 5 1 400 20 5 15 320 39 4 7 72 60 8 6 272 20 5 8 94 58 7 3 190 40 8 11 235 27 9 8 139 30 7 5Explanation / Answer
a. Is the information used in this analysis, cross-sectional data or time series data?
ans : The data is not collected over different points of time. so, the data is not a time series data.
b. State you’re a priori hypothesis about the sign of the slope for each independent variable. (3 pts each)
the null hypothesis is the coeeficients are zero.
c. c. Write out the estimated regression equation using variable specific names? (5 pts)
cost =427.194 -4.583 temperature -14.831insul + 6.101age
d
interpretation :
when the covariates are all zero the cost is 427.194
when temperature increases by one unit cost decreases by 4.583
when temperature increases by one unit cost decraeses by 14.831
when temperature increases by one unit cost increases by 6.101
In case of multiple questions we solve only first four parts completely.
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