7. A researcher believes that there is a relationship between caffeine consumption and creativity. Caffeine consumption is the predictor (X) variable, and creativity scores are the criterion (Y) variable. Caffeine consumption is number of cups of coffee consumed and creativity was rated on a scale 1-10. (a) Compute the linear regression equation. (b) Compute and interpret the standard error of the estimate. Participant Caffeine (X) Creativity (Y ) 119232333426518641
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- Show that an interaction term of a dummy variable and a regressor changes the slope of a regression line..4. Housing Prices in New YorkWe have looked at predicting the price (in s) of New York homes based on the size (in thousands of square feet), using the data in HomesForSaleNY. Two other variables in the dataset are the number of bedrooms and the number of bathrooms. Use technology to create a multiple regression model to predict price based on all three variables: size, number of bedrooms, and number of bathrooms. Price Size Beds Baths 145 1.3 3 1.5 875 2.9 7 3.75 300 1.5 3 2.5 370 1.1 2 1 268 1.5 2 2 1399 4.8 6 5 1125 3.1 3 2.5 299 1.4 3 2 110 1.2 3 1 2999 6 7 8 170 1 2 1 269 1.5 3 1.5 150 1 2 1.5 288 1.8 3 2.1 350 1.3 3 2 120 0.9 1 1 309 2.4 4 2.5 1500 1.5 2 1.5 635 2.5 4 2.5 350 0.9 2 1 459 1.8 4 2.5 275 2.9 4 1.5 275 1.8 3 2 2500 3.7 3 3 187 1.4 3 1.5 238 1.7 3 1.5 155 0.7 1 1 175 1.6 3 1.5 569 3.2 4 2 105 1.2 2 2.5 a) Which of the variables which are significant at the 5% level? b) Which variable is the most…Suppose you a manager for a local car dealership, and you want to use a linear regression model to predict the price of a used car. You decide to use four predictor variables - "Age' (how long the car has been in use since it was produced), "Dents" (the number of visible dents on the outside of the car), "Accidents" (the number of accidents the car has been in), and "mpg" (the fuel efficiency of the car, measured in miles per gallon). Your dataset contains this information for the past 120 cars sold at your dealership. Using this model, your analysis finds an R² of 37%. What is the F statistic of your analysis? Note: 1- Only round your final answer. Round your final answer to two decimal places.
- Online clothes II For the online clothing retailer dis-cussed in the previous problem, the scatterplot of Total Yearly Purchases by Income showsThe correlation between Total Yearly Purchases and Incomeis 0.722. Summary statistics for the two variables are: a) What is the linear regression equation for predictingTotal Yearly Purchase from Income? b) Do the assumptions and conditions for regression ap-pear to be met? c) What is the predicted average Total Yearly Purchasefor someone with a yearly Income of $20,000? Forsomeone with an annual Income of $80,000?d) What percent of the variability in Total YearlyPurchases is accounted for by this model?e) Do you think the regression might be a useful one forthe company? Comment.Explain why the predictor variable is useless as a predictor of the response variable if the slope of the population regression line is 0.Zagat’s publishes restaurant ratings for various locations in the United States. The following table contains the Zagat rating for food, décor, service, and the cost per person for a sample of 100 restaurants located in New York City and in a suburb of New York City. Develop a regression model to predict the cost per person, based on a variable that represents the sum of the ratings for food, décor, and service. Predict the mean cost per person for a restaurant with a sum-mated rating of 50. What should you tell the owner of a group of restaurants in this geographical area about the relationship between the summated rating and the cost of a meal? Location Food Décor Service Summated Rating Coded Location Cost Bins Midpoints City 22 14 19 55 0 33 19.99 25 City 20 15 20 55 0 26 29.99 35 City 23 19 21 63 0 43 39.99 45 City 19 18 18 55 0 32 49.99 55 City 24 16 18 58 0 44 59.99 65 City 22 22 21 65 0 44 69.99 75 City 22 20 20 62 0 50 79.99 85 City 20 19…
- What is the relationship between diamond price and carat size? 307 diamonds were sampled and a straight-line relationship was hypothesized between y = diamond price (in dollars) and x = size of the diamond (in carats). The simple linear regression for the analysis is shown below: Least Squares Linear Regression of PRICE Interpret the standard deviation of the regression model. a) We expect most of the sampled diamond prices to fall within $1117.56 of their least squares predicted values. b) We can explain 89.25% of the variation in the sampled diamond prices around their mean using the size of the diamond in a linear model. c) For every 1-carat increase in the size of a diamond, we estimate that the price of the diamond will increase by $1117.56. d) We expect most of the sampled diamond prices to fall within $2235.12 of their least squares predicted values.Do movies of different types have different rates of return on their budgets? Here's a regression of USGross (SM) on Budget for comedies and action movies with an indicator variable. Complete parts (a) through (d). Dependent variable is: USGross ($M) Coefficient SE(Coeff) - 6.78278 16.95 1.00523 Variable Constant Budget ($M) Comedy 24.0373 0.1613 11.73 t-ratio P-value -0.400 0.6907 6.23 <0.0001 2.05 0.0451 a) Write out the regression model. USGross = + ( Budget + (Comedy R-squared = 32.8% R-squared (adjusted) = 31.0% s = 47.51 55 degrees of freedomXYZ company is interested in quantifying the impact of consumer promotions on the sales of its packaged food product. XYZ has historical data on the following variables for 38 weeks:• Sales: Weekly sales volume in thousands of units.• Prom: Weekly spending on consumer promotions in thousands of Dollars""A regression analysis was applied to XYZ historical dataset. The dependent variable is weekly Sales and the independent variables are weekly Prom and weekly Lagged Prom (i.e., last week Prom). This is a summary of the regression output:Sales = 0.80 + 1.20*Prom - 0.40*Lag(Prom)• R-squared=0.85• F-Statistic=23.83• p-value=0.001 (for the overall regression)•All regression coefficients are statistically significant at the 5% level."A. What is the percent of variance in sales that is explained by Prom and Lag(Prom)? B. Is the overall regression equation statistically significant at the 5% level? Give reasons for the same? C. What is the net volume impact of an incremental $1000 spending per…