Bone mineral density and cola consumption has been recorded for a sample of patients. Let 𝑥 represent the number of colas consumed per week and 𝑦 the bone mineral density in grams per cubic centimeter. Based on the data shown below answer the questions rounding your final answers to four decimal places.(a) Create a scatter plot with linear regression line for the data. (2 points)y = x + (b) Interpret the slope of the regression equation in a complete sentence.

The table below show data that has been collected from different fields from various farms in a certain valley. The table contains the grams of Raspberries tested and the amount of their Vitamin C content in mg. Find a linear model that express Vitamin C content as a function of the weight of the Raspberries.grams Vitamin Ccontent in mg50 9.460 13.970 18.380 22.890 27100 31.7110 37.2A)  Find the regression equation:     𝑦= 𝑥+   Round your answers to 3 decimal places B)  Answer the following questions using your un-rounded regression equation.  If we test 140 grams of raspberries what is the expected Vitamin C content?   𝑚𝑔 (round to the nearest tenth)

Question 8You know that there is a strong correlation between the consumption of ice cream and body weight. The Pearson's r = 0.78. You also know that the average consumption of ice cream per week is five grams with a standard deviation of 1.5 grams. The average weight is 65 kg with a standard deviation of 15 kg. What is the formula of the regression line?1 pointŷ = 26 + 7.8x ŷ = 7.8 + 26xŷ = -502 + 0.078x ŷ = 0.078 - 502x

A consumer's spending is widely believed to be a function of their income. To estimate this relationship, a university professor randomly selected 19 of his students and collected information on their spending (Y, in dollars) and income (X, in dollars) patterns in week 6 of the semester. Assuming a linear relationship between Y and X, the professor used the least-squares method and found that the Y intercept = 20.90 and the slope = 0.66. Based on this information, the slope should be interpreted as: a. For each increase of $1 in a student's weekly income, his/her mean value of weekly spending is estimated to increase by $0.66 (or 66 cents). b. For each increase of $1in a student's weekly spending, his/her mean value of weekly income is estimated to increase by $0.66 (or 66 cents). c. For each increase of $1 in a student's daily income, his/her mean value of daily spending is estimated to increase by 0.66 cents. d. For each increase of $1in a student's weekly income, his/her mean value of weekly spending is estimated to increase by $20.90.

Write down the estimated regression equation for the relationship between temperature and ice cream sales and provide an interpretation of the slope coefficient.

Data for price and thickness of soap is entered into a statistics software package and results in a regression equation of ŷ = 0.4 + 0.2x.What is the correct interpretation of the slope if the price is the response variable and the thickness is an explanatory variable?The price of the soap increases by $0.20, on average, when the thickness increases by 1 cm.The price of the soap decreases by $0.40, on average, when the thickness increases by 1 cm.The price of the soap decreases by $0.20, on average, when the thickness increases by 1 cm.The price of the soap increases by $0.40, on average, when the thickness increases by 1 cm.