Question

Suppose a marketing researcher gathers data on a sample of 200 companies and obtains data on the number of products sold (y), as well as the amount of money spent advertising on Youtube, Facebook, and newspapers (in thousands of dollars). #t Call: #1m(formula youtube + facebook +newspaper, data sales marketing) #Residuals: Min 1Q Median 0.29 30 Max *# -10.59 -1.07 1.43 3.40 ## Coefficients: Estimate Std. Error t value Pr (>|tl) # (Intercept) 3.52667 0.37429 9.42 <2e-16 ** youtube facebook ## newspaper 0.04576 0.00139 32.81 <2e-16 *** 0.18853 0.00861 21.89 <2e-16 -0.00104 0.00587 -0.18 0.86 Signif. codes: ## 0 0.01 0.05 . 0.1 1 0.001 ## Residual atandard error: 2.02 on 196 degrees of freedom ## Multiple R-squared: # F-atatistic: 0.897, Adjusted R-squared: p-value: <2e-16 0.896 570 on 3 and 196 DF, Interpret this model as fully as possible, making sure to assess model fit (the F-statistic and R-squared), write out the equation, identify the statistically significant predictors, and interpret each of them.

Answer 1

From the results the equation can be written as

sales = 3.523 + 0.046* youtube +0.188*facebook - 0.001*newspapers

H₀: All slope coefficients are zero

H₁ : Slope coefficients not equal to zero.

We see that the F-statistic = 570 and its p-value is 2e-16 which is zero. Since p-vale is less than level of significance 0.05 we reject null hypothesis and conclude that the overall regression is significant. Which means there exists a linear relationship between the variables.

from the individual test results, the p-values for coefficient, facebook ad youtube are 0 hence we reject null hypothesis and conclude that these variables are linearly associated with sales. The p-value for news paper coefficient is 0.86 which is greater than 0.05 so we fail to reject null hypothesis and conclude that newspaper is not linearly associated with sales.

R-squared value = 0.897 which says that the model explains the 89.7% of the varaibility between the data.

Interpretation of coefficients:-

i) Intercept: when there are no advertisements the sales were 3.523.

ii) facebook coefficient: With increase in 1 unit of marketing in facebook keeping others constant the sales increases by 0.188 units

iii) youtube coefficient: With increase in 1 unit of marketing in youtube keeping others constant the sales increases by 0.046 units

iv) Newspaper coefficient: With increase in 1 unit of marketing in newspaper keeping others constant the sales decreases by 0.001 units